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lsblh7mf | physics | electrostatics | electric-charges-and-coulomb's-law | Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle $\theta$ with each other. When suspended in water the angle remains the same. If density of the material of the sphere is $1.5 \mathrm{~g} / \mathrm{cc}$, the dielectric constant of water will be __________.<br/><br/> (Ta... | [] | null | 3 | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lsrmbvjf/d3342755-760a-4a06-b677-ad719d5d05b9/2934cca0-ce6c-11ee-bec8-1b5b622d3f34/file-6y3zli1lsrmbvjg.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/6y3zli1lsrmbvjf/d3342755-760a-4a06-b677-ad719d5d05b9/2934cca0-ce6c-11ee-be... | integer | jee-main-2024-online-1st-february-morning-shift | 10,678 |
1lsg74bfk | physics | electrostatics | electric-charges-and-coulomb's-law | <p>Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $$37^{\circ}$$ with each other. When suspended in a liquid of density $$0.7 \mathrm{~g} / \mathrm{cm}^3$$, the angle remains same. If density of material of the sphere is $$1.4 \mathrm{~g} / \mathrm{cm}^3$$, the die... | [] | null | 2 | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lsoisih0/d9aade95-6651-4b12-86db-5e337763a237/f9674440-ccb7-11ee-8ef5-472d1767d2da/file-6y3zli1lsoisih1.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/6y3zli1lsoisih0/d9aade95-6651-4b12-86db-5e337763a237/f9674440-ccb7-11ee... | integer | jee-main-2024-online-30th-january-evening-shift | 10,681 |
lv5grvxd | physics | electrostatics | electric-charges-and-coulomb's-law | <p>Two charged conducting spheres of radii $$a$$ and $$b$$ are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:</p> | [{"identifier": "A", "content": "$$a b$$\n"}, {"identifier": "B", "content": "$$\\frac{b}{a}$$\n"}, {"identifier": "C", "content": "$$\\frac{a}{b}$$\n"}, {"identifier": "D", "content": "$$\\sqrt{a b}$$"}] | ["C"] | null | <p>When two conducting spheres of radii $$a$$ and $$b$$ are connected by a conducting wire, they come to the same potential because conductors in contact share charges until their potentials become equal. The potential of a charged sphere is given by $$V = \frac{kQ}{R}$$, where $$V$$ is the potential, $$k$$ is Coulomb'... | mcq | jee-main-2024-online-8th-april-morning-shift | 10,682 |
lv7v3kbz | physics | electrostatics | electric-charges-and-coulomb's-law | <p>In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of :</p> | [{"identifier": "A", "content": "10<sup>19</sup>"}, {"identifier": "B", "content": "10<sup>39</sup>"}, {"identifier": "C", "content": "10<sup>29</sup>"}, {"identifier": "D", "content": "10<sup>36</sup>"}] | ["B"] | null | <p>To find the ratio of the Coulombic force to the gravitational force between an electron and a proton in a hydrogen-like system, we use the formulae for both forces and then divide them.</p>
<p>The Coulombic (electrostatic) force, $F_C$, between two charges is given by Coulomb's law:</p>
<p>$F_C = k \frac{|q_1 q_2|... | mcq | jee-main-2024-online-5th-april-morning-shift | 10,683 |
lv9s23t6 | physics | electrostatics | electric-charges-and-coulomb's-law | <p>The vehicles carrying inflammable fluids usually have metallic chains touching the ground:</p> | [{"identifier": "A", "content": "To protect tyres from catching dirt from ground\n"}, {"identifier": "B", "content": "It is a custom\n"}, {"identifier": "C", "content": "To alert other vehicles\n"}, {"identifier": "D", "content": "To conduct excess charge due to air friction to ground and prevent sparking"}] | ["D"] | null | <p>The correct option is <strong>Option D: To conduct excess charge due to air friction to ground and prevent sparking</strong>.</p>
<p>This method is grounded in the principles of physics, particularly relating to static electricity and grounding. As vehicles move through the air, especially at high speeds, friction ... | mcq | jee-main-2024-online-5th-april-evening-shift | 10,684 |
lvb29ebb | physics | electrostatics | electric-charges-and-coulomb's-law | <p>Two identical conducting spheres P and S with charge Q on each, repel each other with a force $$16 \mathrm{~N}$$. A third identical uncharged conducting sphere $$\mathrm{R}$$ is successively brought in contact with the two spheres. The new force of repulsion between $$\mathrm{P}$$ and $$\mathrm{S}$$ is :</p> | [{"identifier": "A", "content": "1 N"}, {"identifier": "B", "content": "6 N"}, {"identifier": "C", "content": "12 N"}, {"identifier": "D", "content": "4 N"}] | ["B"] | null | <p>$$\begin{aligned}
& F_1=\frac{K Q^2}{r^2}=16 \mathrm{~N} \\
& F_2=\frac{K\left(\frac{Q}{2}\right)\left(\frac{3}{4}\right)}{r^2}=\frac{3}{8} \times 16=6 \mathrm{~N}
\end{aligned}$$</p>
<p>Final charges on spheres are $$\frac{Q}{2}$$ and $$\frac{3 Q}{4}$$.</p> | mcq | jee-main-2024-online-6th-april-evening-shift | 10,685 |
OFRdGv9vf0OAf0OA | physics | electrostatics | electric-dipole | An electric dipole is placed at an angle of $${30^ \circ }$$ to a non-uniform electric field. The dipole will experience | [{"identifier": "A", "content": "a translation force only in the direction of the field "}, {"identifier": "B", "content": "a translation force only in a direction normal to the direction of the field "}, {"identifier": "C", "content": "a torque as well as a translational force"}, {"identifier": "D", "content": "a torq... | ["C"] | null | <img class="question-image" src="https://imagex.cdn.examgoal.net/lSSuraUDM0v2yQv6N/vxj8MNbpFMfDbgUclOxathUPNYfpg/PFyUvUiYaSVEWiGxY485K2/image.svg" loading="lazy" alt="AIEEE 2006 Physics - Electrostatics Question 203 English Explanation">
<br><br>The electric field will be different at the location of the two charges. ... | mcq | aieee-2006 | 10,686 |
Fo1ZOjOFhYHueuPb | physics | electrostatics | electric-dipole | An electric dipole has a fixed dipole moment $$\overrightarrow p $$, which makes angle $$\theta$$ with respect to x-axis. When
subjected to an electric field $$\mathop {{E_1}}\limits^ \to = E\widehat i$$ , it experiences a torque $$\overrightarrow {{T_1}} = \tau \widehat k$$ . When subjected to another electric
fie... | [{"identifier": "A", "content": "90<sup>o</sup>"}, {"identifier": "B", "content": "45<sup>o</sup>"}, {"identifier": "C", "content": "30<sup>o</sup>"}, {"identifier": "D", "content": "60<sup>o</sup>"}] | ["D"] | null | <br><br>Torque experienced by the dipole in an
electric field,
<br><br>$$T $$ = pE sin$$\theta $$
<br><br>$$\overrightarrow T = \overrightarrow p \times \overrightarrow E $$
<br><br>$$\overrightarrow p = p\cos \theta \widehat i + p\sin \theta \widehat j$$
<br><br>$$\mathop {{E_1}}\limits^ \to = E\widehat i$$
<b... | mcq | jee-main-2017-offline | 10,687 |
q43QhB5cMFJGQJcqBWaNv | physics | electrostatics | electric-dipole | Two electric dipoles, A, B with respective dipole moments $${\overrightarrow d _A} = - 4qai$$ and $${\overrightarrow d _B} = - 2qai$$ are placed on the x-axis with a separation R, as shown in the figure. The distance from A at which both of them produce the same potential is -
<br/><br/><img src="data:image/png;base6... | [{"identifier": "A", "content": "$${{\\sqrt 2 R} \\over {\\sqrt 2 + 1}}$$"}, {"identifier": "B", "content": "$${R \\over {\\sqrt 2 + 1}}$$"}, {"identifier": "C", "content": "$${{\\sqrt 2 R} \\over {\\sqrt 2 - 1}}$$"}, {"identifier": "D", "content": "$${R \\over {\\sqrt 2 - 1}}$$"}] | ["C"] | null | V $$ = {{4qa} \over {\left( {R + x} \right)}} = {{2qa} \over {\left( {{x^2}} \right)}}$$
<br><br>$$\sqrt 2 x = R + x$$
<br><br>$$x = {R \over {\sqrt 2 - 1}}$$
<br><br><img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265033/exam_images/v7c2xqdvcna2hsdlto2h.webp" style="max-width: 100%; height: auto;dis... | mcq | jee-main-2019-online-10th-january-morning-slot | 10,688 |
KPaeYrItv8MFtB7YxFggo | physics | electrostatics | electric-dipole | Charges –q and +q located at A and B, respectively, constitude an electric dipole. Distance AB = 2a, O is the mid point of the dipole and OP is perpendicular to AB. A charge Q is placed at P where OP = y and y >> 2a. The charge Q experiences an electrostatic force F. If Q is now moved along the equatorial line to... | [{"identifier": "A", "content": "9F"}, {"identifier": "B", "content": "3F"}, {"identifier": "C", "content": "F/3"}, {"identifier": "D", "content": "27F"}] | ["D"] | null | Electric field of equitorial plane of dipole
<br><br>$$ = - {{K\overrightarrow P } \over {{r^3}}}$$
<br><br>$$ \therefore $$ At P, F $$ = - {{K\overrightarrow P } \over {{r^3}}}$$Q.
<br><br>At P<sup>1</sup> , F<sup>1</sup> $$ = - {{K\overrightarrow P Q} \over {{{\left( {r/3} \right)}^3}... | mcq | jee-main-2019-online-10th-january-evening-slot | 10,689 |
xrVhiRfWRwCdqiWVtFmi3 | physics | electrostatics | electric-dipole | An electric field of 1000 V/m is applied to an electric dipole at angle of 45<sup>o</sup>. The value of electric dipole moment is 10<sup>–29</sup> C.m. What is the potential energy of the electric dipole? | [{"identifier": "A", "content": "- 7 $$ \\times $$ 10<sup>\u201327</sup> J"}, {"identifier": "B", "content": "$$-$$ 9 $$ \\times $$ 10<sup>\u201320</sup> J"}, {"identifier": "C", "content": "$$-$$ 10 $$ \\times $$ 10<sup>\u201329</sup> J"}, {"identifier": "D", "content": "$$-$$ 20 $$ \\times $$ 10<sup>\u201318</sup> J"... | ["A"] | null | U = $$-$$ $$\overrightarrow P .\overrightarrow E $$
<br><br>= $$-$$ PE cos $$\theta $$
<br><br>= $$-$$ (10<sup>$$-$$29</sup>) (10<sup>3</sup>) cos 45<sup>o</sup>
<br><br>= $$-$$ 0.707 $$ \times $$ 10<sup>$$-$$26</sup> J
<br><br>= $$-$$ 7 $$ \times $$ 10<sup>$$-$$27</sup> J. | mcq | jee-main-2019-online-11th-january-evening-slot | 10,690 |
0GQFGTJppKQvxVmUEmeUg | physics | electrostatics | electric-dipole | Determine the electric dipole moment of the system of the three charges, placed on the vertices of an equilateral triangle, as shown in the figure :
<br/><br/><img src="data:image/png;base64,UklGRhANAABXRUJQVlA4IAQNAAAQjwCdASpRAvwBP4HA2GY2L6ynIZDY4sAwCWlu40WUiymO/Hz68f9n2OLZ99h/3DnY6232eNCmd/ZTBseU72H77/8t/uGrxLp5/ULJ... | [{"identifier": "A", "content": "$$2q\\ell \\widehat j$$"}, {"identifier": "B", "content": "$$\\left( {q\\ell } \\right){{\\widehat i + \\widehat j} \\over {\\sqrt 2 }}$$"}, {"identifier": "C", "content": "$$\\sqrt 3 \\,q\\ell {{\\widehat j - \\widehat i} \\over {\\sqrt 2 }}$$"}, {"identifier": "D", "content": "$$ - \\... | ["D"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734267415/exam_images/l7doasijp5zqm8laviug.webp" style="max-width: 100%; height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2019 (Online) 12th January Morning Slot Physics - Electrostatics Question 159 English Explanation">
<br>$$\lef... | mcq | jee-main-2019-online-12th-january-morning-slot | 10,691 |
7qGBQI5g6FaUnFhE4H3rsa0w2w9jx3b0zg2 | physics | electrostatics | electric-dipole | Shown in the figure is a shell made of a conductor. It has inner radius a and outer radius b, and carries charge
Q. At its centre is a dipole $$\overrightarrow P $$
as shown. In this case :
<img src="data:image/png;base64,UklGRtgMAABXRUJQVlA4IMwMAABQSACdASrkALcAPm00lkckIyIhKjTKAIANiWlu/HyY/etPpv/TO0L/F/17vLfRf33+s/uV/... | [{"identifier": "A", "content": "surface charge density on the inner surface is uniform and equal to $${{\\left( {Q/2} \\right)} \\over {4\\pi {a^2}}}$$"}, {"identifier": "B", "content": "surface charge density on the inner surface of the shell is zero everywhere"}, {"identifier": "C", "content": "surface charge densit... | ["D"] | null | Total charge of dipole = 0, so charge induced on
outside surface = 0.<br><br>
But due to non uniform electric field of dipole, the
charge induced on inner surface is non zero and non
uniform.<br><br>
So, for any observer outside the shell, the resultant
electric field is due to Q uniformly distributed on outer
surface ... | mcq | jee-main-2019-online-12th-april-morning-slot | 10,692 |
Ucp9nRTjEoC3IHY8Fo3rsa0w2w9jx3mppe4 | physics | electrostatics | electric-dipole | A point dipole $$\overrightarrow p = - {p_0}\widehat x$$
is kept at the origin. The potential and electric field due to this dipole on the
y-axis at a distance d are, respectively: (Take V= 0 at infinity) | [{"identifier": "A", "content": "$${{\\left| {\\overrightarrow p } \\right|} \\over {4\\pi { \\in _0}{d^2}}},{{ - \\overrightarrow p } \\over {4\\pi { \\in _0}{d^3}}}$$"}, {"identifier": "B", "content": "$$0,{{\\overrightarrow p } \\over {4\\pi { \\in _0}{d^3}}}$$"}, {"identifier": "C", "content": "$${{\\left| {\\overr... | ["D"] | null | V = 0<br><br>
$$E = - {{K\overrightarrow P } \over {{r^3}}}$$<br><br>
$$ = - {{\overrightarrow p } \over {4\pi {\varepsilon _0}{d^3}}}$$ | mcq | jee-main-2019-online-12th-april-morning-slot | 10,693 |
HVoH4xklgH9aXRqiaG7k9k2k5imsmyi | physics | electrostatics | electric-dipole | An electric dipole of moment
<br/>$$\overrightarrow p = \left( { - \widehat i - 3\widehat j + 2\widehat k} \right) \times {10^{ - 29}} $$ C.m is <br/>at the origin
(0, 0, 0). The electric field due to this dipole at
<br/>$$\overrightarrow r = + \widehat i + 3\widehat j + 5\widehat k$$ (note that $$\overrightarrow r ... | [{"identifier": "A", "content": "$$\\left( { + \\widehat i + 3\\widehat j - 2\\widehat k} \\right)$$"}, {"identifier": "B", "content": "$$\\left( { + \\widehat i - 3\\widehat j - 2\\widehat k} \\right)$$"}, {"identifier": "C", "content": "$$\\left( { - \\widehat i + 3\\widehat j - 2\\widehat k} \\right)$$"}, {"identifi... | ["A"] | null | Since $$\overrightarrow r $$
and $$\overrightarrow p $$
are perpendicular to each other
therefore point lies on the equitorial plane.
Therefore electric field at the point will be
antiparallel to the dipole moment.
<br><br>$$ \therefore $$ $$\overrightarrow E || - \overrightarrow p $$
<br><br>$$ \Rightarrow $$ $$\overr... | mcq | jee-main-2020-online-9th-january-morning-slot | 10,694 |
U61buzOgQTZ10HCEVejgy2xukg0hgwyh | physics | electrostatics | electric-dipole | Two identical electric point dipoles have dipole moments $${\overrightarrow p _1} = p\widehat i$$ and $${\overrightarrow p _2} = - p\widehat i$$ and are held on the x
axis at distance '$$a$$' from each other. When released, they move along the x-axis with the direction
of their dipole moments remaining unchanged. If t... | [{"identifier": "A", "content": "$${p \\over a}\\sqrt {{3 \\over {2\\pi { \\in _0}ma}}} $$"}, {"identifier": "B", "content": "$${p \\over a}\\sqrt {{1 \\over {\\pi { \\in _0}ma}}} $$"}, {"identifier": "C", "content": "$${p \\over a}\\sqrt {{1 \\over {2\\pi { \\in _0}ma}}} $$"}, {"identifier": "D", "content": "$${p \\ov... | ["C"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734267542/exam_images/r7jew9joncb4qsxk3vq0.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 6th September Evening Slot Physics - Electrostatics Question 126 English Explanation">
<br><br>Usi... | mcq | jee-main-2020-online-6th-september-evening-slot | 10,695 |
4YUwG2C3IiqkuiCYhp1klula5r4 | physics | electrostatics | electric-dipole | Given below are two statements: <br/><br/>Statement I : An electric dipole is placed at the center of a hollow sphere. The flux of the electric field through the sphere is zero but the electric field is not zero anywhere in the sphere.<br/><br/>Statement II : If R is the radius of a solid metallic sphere and Q be the t... | [{"identifier": "A", "content": "Both Statement I and Statement II are true"}, {"identifier": "B", "content": "Statement I is false but Statement II is true"}, {"identifier": "C", "content": "Statement I is true but Statement II is false"}, {"identifier": "D", "content": "Both Statement I and Statement II are false"}] | ["C"] | null | <p>Net charge on electric dipole = + q $$-$$ q = 0</p>
<p>Hence, according to Gauss's law,</p>
<p>Electric flux, $$\phi = {{{q_{net}}} \over {{\varepsilon _0}}} = {0 \over {{\varepsilon _0}}} = 0$$</p>
<p>Electric field due to electric dipole is non-zero and varies at point to point.</p>
<p>Hence, statement I is true.... | mcq | jee-main-2021-online-26th-february-evening-slot | 10,696 |
1krsumx7v | physics | electrostatics | electric-dipole | An electric dipole is placed on x-axis in proximity to a line charge of linear charge density 3.0 $$\times$$ 10<sup>$$-$$6</sup> C/m. Line charge is placed on z-axis and positive and negative charge of dipole is at a distance of 10 mm and 12 mm from the origin respectively. If total force of 4N is exerted on the dipole... | [{"identifier": "A", "content": "0.485 mC"}, {"identifier": "B", "content": "815.1 nC"}, {"identifier": "C", "content": "8.8 $$\\mu$$C"}, {"identifier": "D", "content": "4.44 $$\\mu$$C"}] | ["D"] | null | <picture><source media="(max-width: 320px)" srcset="https://res.cloudinary.com/dckxllbjy/image/upload/v1734264144/exam_images/nln9idpezzcedzkzyo7w.webp"><source media="(max-width: 500px)" srcset="https://res.cloudinary.com/dckxllbjy/image/upload/v1734267490/exam_images/s2mjbdpwpaxunoueq47e.webp"><source media="(max-wid... | mcq | jee-main-2021-online-22th-july-evening-shift | 10,697 |
1krw9cz57 | physics | electrostatics | electric-dipole | Two ideal electric dipoles A and B, having their dipole moment p<sub>1</sub> and p<sub>2</sub> respectively are placed on a plane with their centres at O as shown in the figure. At point C on the axis of dipole A, the resultant electric field is making an angle of 37$$^\circ$$ with the axis. The ratio of the dipole mom... | [{"identifier": "A", "content": "$${3 \\over 8}$$"}, {"identifier": "B", "content": "$${3 \\over 2}$$"}, {"identifier": "C", "content": "$${2 \\over 3}$$"}, {"identifier": "D", "content": "$${4 \\over 3}$$"}] | ["C"] | null | <picture><source media="(max-width: 320px)" srcset="https://res.cloudinary.com/dckxllbjy/image/upload/v1734264229/exam_images/bys4p3eeu9ux8qa6twbo.webp"><source media="(max-width: 500px)" srcset="https://res.cloudinary.com/dckxllbjy/image/upload/v1734263471/exam_images/qs76ui4kwi28aw2jdo95.webp"><source media="(max-wid... | mcq | jee-main-2021-online-25th-july-evening-shift | 10,698 |
1l58bt72a | physics | electrostatics | electric-dipole | <p>Given below two statements : One is labelled as Assertion (A) and other is labelled as Reason (R).</p>
<p>Assertion (A) : Non-polar materials do not have any permanent dipole moment.</p>
<p>Reason (R) : When a non-polar material is placed in an electric field, the centre of the positive charge distribution of it's i... | [{"identifier": "A", "content": "Both (A) and (R) are correct and (R) is the correct explanation of (A)."}, {"identifier": "B", "content": "Both (A) and (R) are correct and (R) is not the correct explanation of (A)."}, {"identifier": "C", "content": "(A) is correct but (R) is not correct."}, {"identifier": "D", "conten... | ["C"] | null | <p>Non-polar bonds do not have any net dipole moment and are generally formed in compound where there is presence of symmetry.</p>
<p>When non polar material placed in electric field, due to redistribution of charges dipole is formed.</p>
<p>So, (R) is incorrect.</p> | mcq | jee-main-2022-online-26th-june-morning-shift | 10,699 |
1l6mbigl6 | physics | electrostatics | electric-dipole | <p>Two electric dipoles of dipole moments $$1.2 \times 10^{-30} \,\mathrm{Cm}$$ and $$2.4 \times 10^{-30} \,\mathrm{Cm}$$ are placed in two different uniform electric fields of strengths $$5 \times 10^{4} \,\mathrm{NC}^{-1}$$ and $$15 \times 10^{4} \,\mathrm{NC}^{-1}$$ respectively. The ratio of maximum torque experien... | [] | null | 6 | <p>$${{{\rho _1}} \over {{\rho _2}}} = {{{\mu _1}{B_1}\sin 90} \over {{\mu _2}{B_2}\sin 90}}$$</p>
<p>$$ = {{1.2 \times {{10}^{ - 30}} \times 5 \times {{10}^4}} \over {2.4 \times {{10}^{ - 30}} \times 15 \times {{10}^4}}}$$</p>
<p>$$ = {1 \over 6}$$</p> | integer | jee-main-2022-online-28th-july-morning-shift | 10,700 |
1lgrigha1 | physics | electrostatics | electric-dipole | <p>Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R</p>
<p>Assertion A : If an electric dipole of dipole moment $$30 \times 10^{-5} ~\mathrm{C} ~\mathrm{m}$$ is enclosed by a closed surface, the net flux coming out of the surface will be zero.</p>
<p>Reason R : Electr... | [{"identifier": "A", "content": "A is true but R is false"}, {"identifier": "B", "content": "A is false but R is true"}, {"identifier": "C", "content": "Both A and R are true but R is NOT the correct explanation of A"}, {"identifier": "D", "content": "Both A and R are true and R is the correct explanation of A"}] | ["D"] | null | Assertion A: If an electric dipole of dipole moment $$30 \times 10^{-5} ~\mathrm{C} ~\mathrm{m}$$ is enclosed by a closed surface, the net flux coming out of the surface will be zero.<br/><br/>
This statement is true. According to Gauss's Law, the electric flux through a closed surface is proportional to the net charge... | mcq | jee-main-2023-online-12th-april-morning-shift | 10,702 |
1lh02ki8t | physics | electrostatics | electric-dipole | <p>An electric dipole of dipole moment is $$6.0 \times 10^{-6} ~\mathrm{C m}$$ placed in a uniform electric field of $$1.5 \times 10^{3} ~\mathrm{NC}^{-1}$$ in such a way that dipole moment is along electric field. The work done in rotating dipole by $$180^{\circ}$$ in this field will be ___________ $$\mathrm{m J}$$.</... | [] | null | 18 | <p>The work done $W$ in rotating an electric dipole in a uniform electric field is given by:</p>
<p>$W = pE(1 - \cos\theta)$,</p>
<p>where $p$ is the dipole moment, $E$ is the strength of the electric field, and $\theta$ is the angle the dipole is rotated through.</p>
<p>In this case, the dipole moment $p$ is $6.0 \tim... | integer | jee-main-2023-online-8th-april-morning-shift | 10,703 |
1lh30lxvl | physics | electrostatics | electric-dipole | <p>A dipole comprises of two charged particles of identical magnitude $$q$$ and opposite in nature. The mass 'm' of the positive charged particle is half of the mass of the negative charged particle. The two charges are separated by a distance '$$l$$'. If the dipole is placed in a uniform electric field '$$\bar{E}$$'; ... | [{"identifier": "A", "content": "$$\\sqrt{\\frac{3 q E}{2 m l}}$$"}, {"identifier": "B", "content": "$$\\sqrt{\\frac{4 q E}{m l}}$$"}, {"identifier": "C", "content": "$$\\sqrt{\\frac{8 q E}{3 m l}}$$"}, {"identifier": "D", "content": "$$\\sqrt{\\frac{8 q E}{m l}}$$"}] | ["A"] | null | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1lho7gb66/b1ac5890-9696-4252-9e45-79d3bb1d99c8/40771ae0-f2c5-11ed-8447-35082643c601/file-1lho7gb67.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1lho7gb66/b1ac5890-9696-4252-9e45-79d3bb1d99c8/40771ae0-f2c5-11ed-8447-35082643c601/fi... | mcq | jee-main-2023-online-6th-april-evening-shift | 10,704 |
jaoe38c1lscpvd13 | physics | electrostatics | electric-dipole | <p>Two charges of $$-4 \mu \mathrm{C}$$ and $$+4 \mu \mathrm{C}$$ are placed at the points $$\mathrm{A}(1,0,4) \mathrm{m}$$ and $$\mathrm{B}(2,-1,5) \mathrm{m}$$ located in an electric field $$\overrightarrow{\mathrm{E}}=0.20 \hat{i} \mathrm{~V} / \mathrm{cm}$$. The magnitude of the torque acting on the dipole is $$8 \... | [] | null | 2 | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1lt1jkx8u/8b1b83ad-240e-48dd-8158-10998e53159f/3fe9e6e0-d3e1-11ee-b732-196aad4e0551/file-1lt1jkx8v.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1lt1jkx8u/8b1b83ad-240e-48dd-8158-10998e53159f/3fe9e6e0-d3e1-11ee-b732-196aad4e0551... | integer | jee-main-2024-online-27th-january-evening-shift | 10,705 |
1lsgd3mbl | physics | electrostatics | electric-dipole | <p>The electrostatic potential due to an electric dipole at a distance '$$r$$' varies as :</p> | [{"identifier": "A", "content": "$$\\frac{1}{r^3}$$\n"}, {"identifier": "B", "content": "$$\\frac{1}{\\mathrm{r}}$$\n"}, {"identifier": "C", "content": "$$\\frac{1}{r^2}$$"}, {"identifier": "D", "content": "r"}] | ["C"] | null | <p>$$V=\frac{k P \cos \theta}{r^2}$$</p>
<p>& can also checked dimensionally</p> | mcq | jee-main-2024-online-30th-january-morning-shift | 10,706 |
lv9s2ssg | physics | electrostatics | electric-dipole | <p>The electric field at point $$\mathrm{p}$$ due to an electric dipole is $$\mathrm{E}$$. The electric field at point $$\mathrm{R}$$ on equitorial line will be $$\frac{\mathrm{E}}{x}$$. The value of $$x$$ :</p>
<p><img src="data:image/png;base64,UklGRkwMAABXRUJQVlA4IEAMAAAQ4wCdASrlAgADP4HA3GY2MS2nIFPJMsAwCWlu/HRZUHLHZ... | [] | null | 16 | <p>$$\begin{aligned}
& E=\frac{2 k p}{r^3} \\
& E_R=\frac{k p}{(2 r)^3}=\frac{1}{8}\left(\frac{E}{2}\right) \\
& =\frac{E}{16} \\
& \therefore \quad x=16 \\
&
\end{aligned}$$</p> | integer | jee-main-2024-online-5th-april-evening-shift | 10,707 |
9MTD6o50mPdNBFq7 | physics | electrostatics | electric-field-and-electric-field-intensity | A charged oil drop is suspended in a uniform field of $$3 \times {10^4}$$ $$v/m$$ so that it neither falls nor rises. The charge on the drop will be (Take the mass of the charge $$ = 9.9 \times {10^{ - 15}}\,\,kg$$ and $$g = 10\,m/{s^2}$$) | [{"identifier": "A", "content": "$$1.6 \\times {10^{ - 18}}\\,C$$ "}, {"identifier": "B", "content": "$$3.2 \\times {10^{ - 18}}\\,C$$"}, {"identifier": "C", "content": "$$3.3 \\times {10^{ - 18}}\\,C$$"}, {"identifier": "D", "content": "$$4.8 \\times {10^{ - 18}}\\,C$$"}] | ["C"] | null | At equilibrium, electric force on drop balances weight of drop.
<br><br>$$qE = mg \Rightarrow q$$
<br><br>$$ = {{mg} \over E} = {{9.9 \times {{10}^{ - 15}} \times 10} \over {3 \times {{10}^4}}}$$
<br><br>$$ = 3.3 \times {10^{ - 18}}C$$ | mcq | aieee-2004 | 10,709 |
wyelwCFEQvhxLkqf | physics | electrostatics | electric-field-and-electric-field-intensity | Two point charges $$+8q$$ and $$-2q$$ are located at $$x=0$$ and $$x=L$$ respectively. The location of a point on the $$x$$ axis at which the net electric field due to these two point charges is zero is | [{"identifier": "A", "content": "$${L \\over 4}$$ "}, {"identifier": "B", "content": "$$2$$ $$L$$ "}, {"identifier": "C", "content": "$$4$$ $$L$$ "}, {"identifier": "D", "content": "$$8$$ $$L$$"}] | ["B"] | null | $${{ - K2q} \over {{{\left( {x - L} \right)}^2}}} + {{K8q} \over {{x^2}}} = 0 \Rightarrow {1 \over {{{\left( {x - L} \right)}^2}}} = {4 \over {{x^2}}}$$
<br><br>or, $${1 \over {x - L}} = {2 \over x} \Rightarrow x = 2x - 2L$$
<br><br>or, $$x=2L$$ | mcq | aieee-2005 | 10,710 |
mvbKYte7ItRb7XOQ | physics | electrostatics | electric-field-and-electric-field-intensity | A charged ball $$B$$ hangs from a silk thread $$S,$$ which makes angle $$\theta $$ with a large charged conducting sheet $$P,$$ as shown in the figure. The surface charge density $$\sigma $$ of the sheet is proportional to
<img src="data:image/png;base64,UklGRmwKAABXRUJQVlA4IGAKAADQUgCdASrXAUsBPm02mUkkIyghIRTY6QANiWlu... | [{"identifier": "A", "content": "$$\\cot \\,\\theta $$ "}, {"identifier": "B", "content": "$$\\cos \\,\\theta $$ "}, {"identifier": "C", "content": "$$\\tan \\,\\theta $$ "}, {"identifier": "D", "content": "$$\\sin \\,\\theta $$ "}] | ["C"] | null | <img class="question-image" src="https://imagex.cdn.examgoal.net/Gc7VjCdjqKosi8ojk/FitQVKQmwSVkSIvsruK6Eov5NWWqK/RFxfN4zk8WLulCmu2exo90/image.svg" loading="lazy" alt="AIEEE 2005 Physics - Electrostatics Question 204 English Explanation">
<br><br>$$T\sin \theta = {\sigma \over {{\varepsilon _0}K}}.q\,\,\,\,\,\,\,\,\,\... | mcq | aieee-2005 | 10,711 |
AB0Kv7W2bWRiftV5 | physics | electrostatics | electric-field-and-electric-field-intensity | A thin spherical shell of radius $$R$$ has charge $$Q$$ spread uniformly over its surface. Which of the following graphs most closely represents the electric field $$E(r)$$ produced by the shell in the range $$0 \le r < \infty ,$$ where $$r$$ is the distance from the center of the shell? | [{"identifier": "A", "content": "<img class=\"question-image\" src=\"https://res.cloudinary.com/dckxllbjy/image/upload/v1734265152/exam_images/neaufod3sps1mhqkykdd.webp\" loading=\"lazy\" alt=\"AIEEE 2008 Physics - Electrostatics Question 197 English Option 1\"> "}, {"identifier": "B", "content": "<img class=\"question... | ["A"] | null | The electric field inside a thin spherical shell of radius $$R$$ has charge $$Q$$ spread uniformly over its surface is zero.
<br><br><img class="question-image" src="https://imagex.cdn.examgoal.net/HHte8BfSHJOQTJFeD/sr2iRK5qxPXxIUyJ1BxObXGJv4dqy/DVvRj7khvZAbIJQZEotErf/image.svg" loading="lazy" alt="AIEEE 2008 Physics -... | mcq | aieee-2008 | 10,712 |
cVELXW3tKHjNNqmz | physics | electrostatics | electric-field-and-electric-field-intensity | Let $$P\left( r \right) = {Q \over {\pi {R^4}}}r$$ be the change density distribution for a solid sphere of radius $$R$$ and total charge $$Q$$. For a point $$'p'$$ inside the sphere at distance $${r_1}$$ from the center of the sphere, the magnitude of electric field is : | [{"identifier": "A", "content": "$${Q \\over {4\\pi \\,{ \\in _0}\\,r_1^2}}$$ "}, {"identifier": "B", "content": "$${{Qr_1^2} \\over {4\\pi \\,{ \\in _0}\\,{R^4}}}$$"}, {"identifier": "C", "content": "$${{Qr_1^2} \\over {3\\pi \\,{ \\in _0}\\,{R^4}}}$$ "}, {"identifier": "D", "content": "$$0$$"}] | ["B"] | null | <img class="question-image" src="https://imagex.cdn.examgoal.net/tiqW9aKqmddagbGAr/b4V9twI4tWYWLeyOCDAebisNjE4uF/YYD86LfwchXuGfn5rM0nDR/image.svg" loading="lazy" alt="AIEEE 2009 Physics - Electrostatics Question 193 English Explanation">
<br><br>Let us consider a spherical shell of thickness $$dx$$ and radius $$x.$$ Th... | mcq | aieee-2009 | 10,713 |
djZbC84NYDv3VYt2 | physics | electrostatics | electric-field-and-electric-field-intensity | Let there be a spherically symmetric charge distribution with charge density varying as $$\rho \left( r \right) = {\rho _0}\left( {{5 \over 4} - {r \over R}} \right)$$ upto $$r=R,$$ and $$\rho \left( r \right) = 0$$ for $$r>R,$$ where $$r$$ is the distance from the erigin. The electric field at a distance $$r\left( ... | [{"identifier": "A", "content": "$${{{\\rho _0}r} \\over {4{\\varepsilon _0}}}\\left( {{5 \\over 3} - {r \\over R}} \\right)$$ "}, {"identifier": "B", "content": "$${{4\\pi {\\rho _0}r} \\over {3{\\varepsilon _0}}}\\left( {{5 \\over 3} - {r \\over R}} \\right)$$ "}, {"identifier": "C", "content": "$${{4{\\rho _0}r} \... | ["A"] | null | <img class="question-image" src="https://imagex.cdn.examgoal.net/kvzezHFULJwKbPuOf/fPGmKYccDI61W2mAR2B1YFqVOJwB1/QsSPLM6oozaTN9yDFVztgQ/image.svg" loading="lazy" alt="AIEEE 2010 Physics - Electrostatics Question 191 English Explanation">
<br><br>Let us consider a spherical shell of radius $$x$$ and thickness $$dx.$$
<... | mcq | aieee-2010 | 10,714 |
cduXhWXrbm08u8bD | physics | electrostatics | electric-field-and-electric-field-intensity | A thin semi-circular ring of radius $$r$$ has a positive charges $$q$$ distributed uniformly over it. The net field $$\overrightarrow E $$ at the center $$O$$ is
<img src="data:image/png;base64,UklGRuoGAABXRUJQVlA4IN4GAAAQQgCdASrZASgBPm02m0kkIyKhITSYqIANiWlu+F+pJ2zT/26a8nm7Z+mf9r/EnwD/u/RVeZD4D8D/QP6N5+f5TwX8gHnB/ve9U... | [{"identifier": "A", "content": "$${q \\over {4{\\pi ^2}{\\varepsilon _0}{r^2}}}\\,j$$ "}, {"identifier": "B", "content": "$$ - {q \\over {4{\\pi ^2}{\\varepsilon _0}{r^2}}}\\,j$$ "}, {"identifier": "C", "content": "$$ - {q \\over {2{\\pi ^2}{\\varepsilon _0}{r^2}}}\\,j$$ "}, {"identifier": "D", "content": "$$ {q \\ov... | ["C"] | null | <img class="question-image" src="https://imagex.cdn.examgoal.net/p3kFNiikGsPhas3Uw/XhCx6ikAza6WNMo8dlAJVzfu71pTj/ZtsTX675GAMG1V0VY9e9yP/image.svg" loading="lazy" alt="AIEEE 2010 Physics - Electrostatics Question 192 English Explanation">
<br><br>Let us consider a differential element $$dl.$$ charge on this element.
<br... | mcq | aieee-2010 | 10,715 |
KZrp7NPtAUeU5Rsj | physics | electrostatics | electric-field-and-electric-field-intensity | In a uniformly charged sphere of total charge $$Q$$ and radius $$R,$$ the electric field $$E$$ is plotted as function of distance from the center. The graph which would correspond to the above will be:
| [{"identifier": "A", "content": "<img class=\"question-image\" src=\"https://res.cloudinary.com/dckxllbjy/image/upload/v1734263760/exam_images/akd2wmt7h1umrohvtuox.webp\" loading=\"lazy\" alt=\"AIEEE 2012 Physics - Electrostatics Question 188 English Option 1\"> "}, {"identifier": "B", "content": "<img class=\"question... | ["C"] | null | $${E_{in}} \propto r$$
<br>$${E_{out}} \propto {1 \over {{r^2}}}$$ | mcq | aieee-2012 | 10,716 |
hgkqbGjnZ0JRMHv42SsFg | physics | electrostatics | electric-field-and-electric-field-intensity | A solid ball of radius R has a charge density $$\rho $$
<br/>given by $$\rho $$ = $$\rho $$<sub>o</sub> (1 $$-$$ $${\raise0.5ex\hbox{$\scriptstyle r$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle R$}}$$) for 0 $$ \le $$ r $$ \le $$ R. The electric field outside the ball is : | [{"identifier": "A", "content": "$${{{\\rho _o}{R^3}} \\over {{ \\in _o}{r^2}}}$$"}, {"identifier": "B", "content": "$${{{\\rho _o}{R^3}} \\over {12{ \\in _o}{r^2}}}$$"}, {"identifier": "C", "content": "$${{4{\\rho _o}{R^3}} \\over {3{ \\in _o}{r^2}}}$$ "}, {"identifier": "D", "content": "$${{3{\\rho _o}{R^3}} \\over {... | ["B"] | null | Electric field outside the ball is given by
<br><br>E = $${1 \over {4\pi {\varepsilon _0}}}{q \over {{r^2}}}$$ .............(i)
<br><br>Now, dq = $$\rho $$dV = $$\rho $$(4$$\pi $$r<sup>2</sup>)dr
<br><br>$$ \therefore $$ q = $$\int {dq = \int\limits_0^R {{\rho _0}\left( {1 - {r \over R}} \right)\left( {4\pi {r^2}} \rig... | mcq | jee-main-2018-online-15th-april-evening-slot | 10,719 |
gGLz6Fg1XP41Br3Q75bBG | physics | electrostatics | electric-field-and-electric-field-intensity | For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance h from its center. Then value of h is : | [{"identifier": "A", "content": "$${R \\over {\\sqrt 5 }}$$"}, {"identifier": "B", "content": "$${R \\over {\\sqrt 2 }}$$"}, {"identifier": "C", "content": "R"}, {"identifier": "D", "content": "R$$\\sqrt 2 $$"}] | ["B"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734263523/exam_images/imqgnxixrtktf3zmqwry.webp" style="max-width: 100%; height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2019 (Online) 9th January Morning Slot Physics - Electrostatics Question 169 English Explanation"><br><br>
Ele... | mcq | jee-main-2019-online-9th-january-morning-slot | 10,720 |
YY3uk84puRG86EYnTW7te | physics | electrostatics | electric-field-and-electric-field-intensity | Four point charges –q, +q, +q and –q are placed
on y-axis at y = –2d, y = –d, y = +d and
y = +2d, respectively. The magnitude of the
electric field E at a point on the x-axis at
x = D, with D >> d, will behave as :- | [{"identifier": "A", "content": "$$E \\propto {1 \\over D^3}$$"}, {"identifier": "B", "content": "$$E \\propto {1 \\over D}$$"}, {"identifier": "C", "content": "$$E \\propto {1 \\over D^4}$$"}, {"identifier": "D", "content": "$$E \\propto {1 \\over D^2}$$"}] | ["C"] | null | Electric field at p = 2E<sub>1</sub>cos$$\theta $$<sub>1</sub> –2E<sub>2</sub>cos$$\theta $$<sub>2</sub><br><br>
= $${{2Kq} \over {\left( {{d^2} + {D^2}} \right)}} \times {D \over {{{\left( {{d^2} + {D^2}} \right)}^{1/2}}}} - {{2Kq} \over {\left[ {{{\left( {2d} \right)}^2} + {D^2}} \right]}} \times {D \over {{{\left[ {... | mcq | jee-main-2019-online-9th-april-evening-slot | 10,721 |
wNC36OiOLMkUBQZmugDD1 | physics | electrostatics | electric-field-and-electric-field-intensity | The bob of a simple pendulum has mass 2g and
a charge of 5.0 μC. It is at rest in a uniform
horizontal electric field of intensity 2000 V/m.
At equilibrium, the angle that the pendulum
makes with the vertical is : (take g = 10 m/s<sup>2</sup>) | [{"identifier": "A", "content": "tan<sup>\u20131</sup>(5.0)"}, {"identifier": "B", "content": "tan<sup>\u20131</sup>(2.0)"}, {"identifier": "C", "content": "tan<sup>\u20131</sup>(0.5)"}, {"identifier": "D", "content": "tan<sup>\u20131</sup>(0.2)"}] | ["C"] | null | Tcos$$\theta $$ = mg<br><br>
Tsin$$\theta $$ = qE<br><br>
tan$$\theta $$ = $${{qE} \over {mg}}$$<br><br>
tan$$\theta $$ = $${{5 \times {{10}^{ - 16}} \times 2000} \over {2 \times {{10}^{ - 3}} \times 10}} = {1 \over 2}$$<br><br>
$$ \Rightarrow $$ $${\tan ^{ - 1}}\left( {{1 \over 2}} \right) = {\tan ^{ - 1}}\left( {0.5}... | mcq | jee-main-2019-online-8th-april-morning-slot | 10,722 |
T2vPSW3gpzKTHuv3NhINP | physics | electrostatics | electric-field-and-electric-field-intensity | Two point charges q<sub>1</sub>$$\left( {\sqrt {10} \mu C} \right)$$ and q<sub>2</sub>($$-$$ 25 $$\mu $$C) are placed on the x-axis at x = 1 m and x = 4 m respectively. The electric field (in V/m) at a point y = 3 m on y-axis is,
<br/>[take $${1 \over {4\pi { \in _0}}}$$ = 9 $$ \times $$ 10<sup>9</sup> Nm<sup>2</sup>C... | [{"identifier": "A", "content": "$$\\left( {63\\widehat i - 27\\widehat j} \\right) \\times {10^2}$$"}, {"identifier": "B", "content": "$$\\left( { - 63\\widehat i + 27\\widehat j} \\right) \\times {10^2}$$"}, {"identifier": "C", "content": "$$\\left( {81\\widehat i - 81\\widehat j} \\right) \\times {10^2}$$"}, {"ident... | ["A"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734267838/exam_images/q5jroq8rpfxgyk8ca7nc.webp" style="max-width: 100%; height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2019 (Online) 9th January Evening Slot Physics - Electrostatics Question 168 English Explanation 1">
<br>Elect... | mcq | jee-main-2019-online-9th-january-evening-slot | 10,723 |
C3dUrFug6o6GxPz33Njgy2xukg0h4wya | physics | electrostatics | electric-field-and-electric-field-intensity | Consider the force F on a charge 'q' due to a uniformly charged spherical shell of radius R carrying
charge Q distributed uniformly over it. Which one of the following statements is true for F, if 'q' is
placed at distance r from the centre of the shell? | [{"identifier": "A", "content": "$${1 \\over {4\\pi {\\varepsilon _0}}}{{qQ} \\over {{R^2}}} > F > 0$$ for r < R"}, {"identifier": "B", "content": "$$F = {1 \\over {4\\pi {\\varepsilon _0}}}{{qQ} \\over {{r^2}}}$$ for r > R"}, {"identifier": "C", "content": "$$F = {1 \\over {4\\pi {\\varepsilon _0}}}{{qQ} \... | ["B"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265987/exam_images/vkiwxwi0hvmzwe61bo4s.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 6th September Evening Slot Physics - Electrostatics Question 127 English Explanation">
<br>Inside ... | mcq | jee-main-2020-online-6th-september-evening-slot | 10,724 |
29FpNiTZ1Zk3JyyQdR7k9k2k5hgt5ci | physics | electrostatics | electric-field-and-electric-field-intensity | A particle of mass m and charge q is released
from rest in a uniform electric field. If there is
no other force on the particle, the dependence
of its speed v on the distance x travelled by it
is correctly given by (graphs are schematic and
not drawn to scale) | [{"identifier": "A", "content": "<img src=\"https://res.cloudinary.com/dckxllbjy/image/upload/v1734266287/exam_images/g30fghp4q84rsdjeuq1h.webp\" style=\"max-width: 100%;height: auto;display: block;margin: 0 auto;\" loading=\"lazy\" alt=\"JEE Main 2020 (Online) 8th January Evening Slot Physics - Electrostatics Question... | ["B"] | null | As F = qE
<br><br>$$ \Rightarrow $$ ma = qE
<br><br>$$ \Rightarrow $$ a = $${{qE} \over m}$$
<br><br>Also we know, v<sup>2</sup> = u<sup>2</sup> + 2as
<br><br>$$ \Rightarrow $$ v<sup>2</sup> = 0 + 2$$\left( {{{qE} \over m}} \right)$$s
<br><br>$$ \Rightarrow $$ v = $${\sqrt {{{2qE} \over m}} \sqrt x }$$ | mcq | jee-main-2020-online-8th-january-evening-slot | 10,726 |
CKw9imxNSehN3xJr8Tjgy2xukfakhzkn | physics | electrostatics | electric-field-and-electric-field-intensity | A particle of charge q and mass m is subjected to an electric field<br/> E = E<sub>0</sub>
(1 – $$a$$x<sup>2</sup>) in the x-direction,
where $$a$$ and E<sub>0</sub>
are constants. Initially the particle was at rest at x = 0. Other than the initial
position the kinetic energy of the particle becomes zero when the dis... | [{"identifier": "A", "content": "$$a$$"}, {"identifier": "B", "content": "$$\\sqrt {{2 \\over a}} $$"}, {"identifier": "C", "content": "$$\\sqrt {{3 \\over a}} $$"}, {"identifier": "D", "content": "$$\\sqrt {{1 \\over a}} $$"}] | ["C"] | null | $$W = \Delta KE$$
<br><br>As inital and final kinetic energy both are zero so $$\Delta KE$$ = 0
<br><br>$$ \therefore $$ W = 0
<br><br>$$ \Rightarrow $$ $$\int\limits_0^x {Fdx} = 0$$<br><br>$$ \Rightarrow $$ $$q\int\limits_0^x {{E_0}\left( {1 - a{x^2}} \right)dx} = 0$$<br><br>$$ \Rightarrow $$ $$q{E_0}\left[ {\int\li... | mcq | jee-main-2020-online-4th-september-evening-slot | 10,727 |
ixfmOCTaPTycxJnA8Kjgy2xukexx58kk | physics | electrostatics | electric-field-and-electric-field-intensity | A small point mass carrying some positive
charge on it, is released from the edge of a
table. There is a uniform electric field in this
region in the horizontal direction. Which of the
following options then correctly describe the
trajectory of the mass?<br/> (Curves are drawn
schematically and are not to scale).
<img ... | [{"identifier": "A", "content": "<img src=\"https://res.cloudinary.com/dckxllbjy/image/upload/v1734263546/exam_images/swxrywcmj42kaqdn20yw.webp\" style=\"max-width: 100%;height: auto;display: block;margin: 0 auto;\" loading=\"lazy\" alt=\"JEE Main 2020 (Online) 2nd September Evening Slot Physics - Electrostatics Questi... | ["A"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734263558/exam_images/ew8ddb6szubol4ex5f9y.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 2nd September Evening Slot Physics - Electrostatics Question 135 English Explanation">
<br><br>Sin... | mcq | jee-main-2020-online-2nd-september-evening-slot | 10,728 |
SDTw5rZDxIKzcesy2fjgy2xukeuurjeu | physics | electrostatics | electric-field-and-electric-field-intensity | A charged particle (mass m and charge q)
<br/>moves along X-axis with velocity V<sub>0</sub>. When it
<br/>passes through the origin it enters a region
having uniform electric field
<br/>$$\overrightarrow E = - E\widehat j$$ which
extends upto x = d. <br/>Equation of path of electron
in the region x > d is
<img s... | [{"identifier": "A", "content": "y = $${{qEd} \\over {mV_0^2}}\\left( {x - d} \\right)$$"}, {"identifier": "B", "content": "y = $${{qEd} \\over {mV_0^2}}\\left( {{d \\over 2} - x} \\right)$$"}, {"identifier": "C", "content": "y = $${{qEd} \\over {mV_0^2}}x$$"}, {"identifier": "D", "content": "y = $${{qE{d^2}} \\over {m... | ["B"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265868/exam_images/k43dp0yfk7wb3cfyrclh.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 2nd September Morning Slot Physics - Electrostatics Question 136 English Explanation">
<br>Let par... | mcq | jee-main-2020-online-2nd-september-morning-slot | 10,729 |
XJQ8QnBw7M1HXMSa5ojgy2xuketxfe7j | physics | electrostatics | electric-field-and-electric-field-intensity | Two charged thin infinite plane sheets of <br/>uniform surface charge density $${\sigma _ + }$$ and $${\sigma _ - }$$, <br/>where |$${\sigma _ + }$$| > |$${\sigma _ - }$$|, intersect at right angle. <br/>Which of the following best represents the
<br/>electric field lines for this system : | [{"identifier": "A", "content": "<img src=\"https://res.cloudinary.com/dckxllbjy/image/upload/v1734267020/exam_images/zcp5frvyjreh7k5kahxi.webp\" style=\"max-width: 100%;height: auto;display: block;margin: 0 auto;\" loading=\"lazy\" alt=\"JEE Main 2020 (Online) 4th September Morning Slot Physics - Electrostatics Questi... | ["B"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734267508/exam_images/fguiyjqdldikdhvwto4q.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 4th September Morning Slot Physics - Electrostatics Question 138 English Explanation">
Given, |$${... | mcq | jee-main-2020-online-4th-september-morning-slot | 10,730 |
oCrTzSojRLTEpHgskH7k9k2k5i7lp01 | physics | electrostatics | electric-field-and-electric-field-intensity | Consider a sphere of radius R which carries a
uniform charge density $$\rho $$. If a sphere of radius $${{R \over 2}}$$ is carved out of it, as shown, the ratio $${{\left| {\overrightarrow {{E_A}} } \right|} \over {\left| {\overrightarrow {{E_B}} } \right|}}$$ of magnitude of electric field $${\overrightarrow {{E_A}} }... | [{"identifier": "A", "content": "$${{17} \\over {54}}$$"}, {"identifier": "B", "content": "$${{18} \\over {54}}$$"}, {"identifier": "C", "content": "$${{18} \\over {34}}$$"}, {"identifier": "D", "content": "$${{21} \\over {34}}$$"}] | ["C"] | null | $$\left| {\overrightarrow {{E_A}} } \right|$$ = (E<sub>complete</sub>)<sub>center</sub> - (E<sub>removed</sub>)<sub>surface</sub>
<br><br>= 0 - $$\left| {{{k\rho {4 \over 3}\pi {{\left( {{R \over 2}} \right)}^3}} \over {{{\left( {{R \over 2}} \right)}^2}}}} \right|$$
<br><br>= $${k\rho {4 \over 3}\pi \left( {{R \over 2... | mcq | jee-main-2020-online-9th-january-morning-slot | 10,731 |
aPFLHh6V4P90Fylmew7k9k2k5gxz7cy | physics | electrostatics | electric-field-and-electric-field-intensity | Three charged particle A, B and C with charges
–4q, 2q and –2q are present on the
circumference of a circle of radius d. the charged
particles A, C and centre O of the circle formed
an equilateral triangle as shown in figure. Electric
field at O along x-direction is :
<img src="data:image/png;base64,UklGRm4SAABXRUJQVlA... | [{"identifier": "A", "content": "$${3{\\sqrt 3 q} \\over 4{\\pi {\\varepsilon _0}{d^2}}}$$"}, {"identifier": "B", "content": "$${{\\sqrt 3 q} \\over 4{\\pi {\\varepsilon _0}{d^2}}}$$"}, {"identifier": "C", "content": "$${{\\sqrt 3 q} \\over {\\pi {\\varepsilon _0}{d^2}}}$$"}, {"identifier": "D", "content": "$${{2\\sqrt... | ["C"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734267332/exam_images/qilyublbmim2zv1yaukk.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 8th January Morning Slot Physics - Electrostatics Question 144 English Explanation">
<br>Resultant... | mcq | jee-main-2020-online-8th-january-morning-slot | 10,732 |
ZdtZam0eJts4BupRCH1klrgu9ke | physics | electrostatics | electric-field-and-electric-field-intensity | A cube of side 'a' has point charges +Q located at each of its vertices except at the origin where the charge is $$-$$Q. The electric field at the centre of cube is :<br/><br/>
<img src="data:image/png;base64,UklGRtgQAABXRUJQVlA4IMwQAACwDQGdASoAA/QCP4HA2GW2L6ypoTH5csAwCWlu4WuS9mNwvj6W9Flxav0xD/Rbpzth1f/uRxBPS1Ut//+sX7/... | [{"identifier": "A", "content": "$${{2Q} \\over {3\\sqrt 3 \\pi {\\varepsilon _0}{a^2}}}\\left( {\\widehat x + \\widehat y + \\widehat z} \\right)$$"}, {"identifier": "B", "content": "$${{ - Q} \\over {3\\sqrt 3 \\pi {\\varepsilon _0}{a^2}}}\\left( {\\widehat x + \\widehat y + \\widehat z} \\right)$$"}, {"identifier": ... | ["D"] | null | We can replace $$-$$ Q charge at origin by + Q and $$-$$ 2Q. Now, due to + Q charge at every corner of cube, electric field at centre of cube is zero. So, net electric field at centre is only due to $$-$$ 2Q charge at origin. Vector form of electric field strength,<br/><br/>$$E = {{Kqr} \over {{r^3}}}$$<br/><br/>Here, ... | mcq | jee-main-2021-online-24th-february-morning-slot | 10,734 |
dTmWHwJSNF20cXOebj1kltiyk3a | physics | electrostatics | electric-field-and-electric-field-intensity | Find the electric field at point P (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length L carrying a charge Q. The distance of the point P from the centre of the rod is a = $${{\sqrt 3 } \over 2}L$$.<br/><br/><img src="data:image/png;base64,UklGRuQFAABXRUJQVlA4INgFAABwLACdASrMAK... | [{"identifier": "A", "content": "$${Q \\over {4\\pi {\\varepsilon _0}{L^2}}}$$"}, {"identifier": "B", "content": "$${Q \\over {3\\pi {\\varepsilon _0}{L^2}}}$$"}, {"identifier": "C", "content": "$${Q \\over {2\\sqrt 3 \\pi {\\varepsilon _0}{L^2}}}$$"}, {"identifier": "D", "content": "$${{\\sqrt 3 Q} \\over {4\\pi {\\va... | ["C"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265213/exam_images/xlv0oquo08gctzsrlpad.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 26th February Morning Shift Physics - Electrostatics Question 117 English Explanation">
<br>$$\tan... | mcq | jee-main-2021-online-26th-february-morning-slot | 10,735 |
inrVo1wwTLtiVNCR161klum8c8m | physics | electrostatics | electric-field-and-electric-field-intensity | An inclined plane making an angle of 30$$^\circ$$ with the horizontal is placed in a uniform horizontal electric field $$200{N \over C}$$ as shown in the figure. A body of mass 1 kg and charge 5 mC is allowed to slide down from rest at a height of 1 m. If the coefficient of friction is 0.2, find the time taken by the b... | [{"identifier": "A", "content": "0.46 s"}, {"identifier": "B", "content": "0.92 s"}, {"identifier": "C", "content": "1.3 s"}, {"identifier": "D", "content": "2.3 s"}] | ["C"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265201/exam_images/pbazdkcwek9pmwobs7qk.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 26th February Evening Shift Physics - Electrostatics Question 115 English Explanation">
<br>f = mg... | mcq | jee-main-2021-online-26th-february-evening-slot | 10,736 |
PXJT3Cd9SpbBiSSPFp1kmipehcv | physics | electrostatics | electric-field-and-electric-field-intensity | Find out the surface charge density at the intersection of point x = 3 m plane and x-axis, in the region of uniform line charge of 8 nC/m lying along the z-axis in free space. | [{"identifier": "A", "content": "0.424 nC m<sup>$$-$$2</sup>"}, {"identifier": "B", "content": "4.0 nC m<sup>$$-$$2</sup>"}, {"identifier": "C", "content": "47.88 C/m"}, {"identifier": "D", "content": "0.07 nC m<sup>$$-$$2</sup>"}] | ["A"] | null | Electric field due to wire is given by $$E = {{2k\lambda } \over r}$$<br><br>Electric field with surface charge density $$E = {\sigma \over {{ \in _0}}}$$<br><br>$${{2k\lambda } \over r} = {\sigma \over {{ \in _0}}}$$<br><br>$$ \Rightarrow 2{1 \over {4\pi { \in _0}}}{\lambda \over r} = {\sigma \over {{ \in _0}}}$$<... | mcq | jee-main-2021-online-16th-march-evening-shift | 10,737 |
RZQXGYTlncPboo7V2Z1kmkqrr6k | physics | electrostatics | electric-field-and-electric-field-intensity | An oil drop of radius 2 mm with a density 3g cm<sup>$$-$$3</sup> is held stationary under a constant electric field 3.55 $$\times$$ 10<sup>5</sup> V m<sup>$$-$$1</sup> in the Millikan's oil drop experiment. What is the number of excess electrons that the oil drop will possess? (consider g = 9.81 m/s<sup>2</sup>) | [{"identifier": "A", "content": "48.8 $$\\times$$ 10<sup>11</sup>"}, {"identifier": "B", "content": "1.73 $$\\times$$ 10<sup>10</sup>"}, {"identifier": "C", "content": "17.3 $$\\times$$ 10<sup>10</sup>"}, {"identifier": "D", "content": "1.73 $$\\times$$ 10<sup>12</sup>"}] | ["B"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265676/exam_images/z50dgjy3i2h18x8nrf7x.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 18th March Morning Shift Physics - Electrostatics Question 111 English Explanation">
<br>F<sub>e</... | mcq | jee-main-2021-online-18th-march-morning-shift | 10,738 |
1krppimvr | physics | electrostatics | electric-field-and-electric-field-intensity | A body having specific charge 8 $$\mu$$C/g is resting on a frictionless plane at a distance 10 cm from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of 100 V/m is applied horizontally towards the wall. If the collision of the body with the wall is perfectly elastic, ... | [] | null | 1 | Given, <br/><br/>q = 8$$\mu$$C/g = 8 $$\times$$ 10<sup>$$-$$6</sup> C/g = 8 $$\times$$ 10<sup>$$-$$3</sup> C/kg<br/><br/>s = 10 cm = 0.1 m $$\Rightarrow$$ E = 100 V/m<br/><br/>We know that, acceleration, a = $${{force(F)} \over {mass(m)}}$$<br/><br/>$$\Rightarrow$$ a = $${{qE} \over m}$$ [$$\because$$ F = qE]<br/><br/>... | integer | jee-main-2021-online-20th-july-morning-shift | 10,739 |
1ks18qmuc | physics | electrostatics | electric-field-and-electric-field-intensity | What will be the magnitude of electric field at point O as shown in the figure? Each side of the figure is l and perpendicular to each other?<br/><br/><img src="data:image/png;base64,UklGRogQAABXRUJQVlA4IHwQAABQZACdASpEAQgBPm00lUikIqShITFbkJANiWlu/EsXu8UDOzrv/SP+Z/jd5jv0f+0fkT4j/m37p+W/pSVi39B5Lfq59f/jf9V/5P9s+dn6L/iv4... | [{"identifier": "A", "content": "$${1 \\over {4\\pi {\\varepsilon _0}}}{q \\over {{l^2}}}$$"}, {"identifier": "B", "content": "$${1 \\over {4\\pi {\\varepsilon _0}}}{q \\over {(2{l^2})}}\\left( {2\\sqrt 2 - 1} \\right)$$"}, {"identifier": "C", "content": "$${q \\over {4\\pi {\\varepsilon _0}{{(2l)}^2}}}$$"}, {"identif... | ["B"] | null | $${E_1} = {{kq} \over {{l^2}}} = {E_2}$$<br><br>$${E_3} = {{kq} \over {{{(\sqrt 2 l)}^2}}} = {{kq} \over {2{l^2}}}$$<br><br>$$E = {{\sqrt 2 kq} \over {{l^2}}} - {{kq} \over {2{l^2}}} = {{kq} \over {2{l^2}}}\left( {2\sqrt 2 - 1} \right)$$<br><br><img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265666/ex... | mcq | jee-main-2021-online-27th-july-evening-shift | 10,740 |
1ktacirh3 | physics | electrostatics | electric-field-and-electric-field-intensity | A solid metal sphere of radius R having charge q is enclosed inside the concentric spherical shell of inner radius a and outer radius b as shown in the figure. The approximate variation electric field $$\overrightarrow E $$ as a function of distance r from centre O is given by <br/><br/><img src="data:image/png;base64,... | [{"identifier": "A", "content": "<img src=\"https://res.cloudinary.com/dckxllbjy/image/upload/v1734265907/exam_images/ungsj8uestkmco5xgnla.webp\" style=\"max-width: 100%;height: auto;display: block;margin: 0 auto;\" loading=\"lazy\" alt=\"JEE Main 2021 (Online) 26th August Morning Shift Physics - Electrostatics Questio... | ["A"] | null | Considering outer spherical shell is non-conducting.<br><br>Electric field inside a metal sphere is zero.<br><br>r < R $$\Rightarrow$$ E = 0<br><br>r > R $$\Rightarrow$$ E = $${{kQ} \over {{r^2}}}$$<br><br><img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734263576/exam_images/otcstoqwckv3ctwyaili.web... | mcq | jee-main-2021-online-26th-august-morning-shift | 10,741 |
1ktdy8xq6 | physics | electrostatics | electric-field-and-electric-field-intensity | A uniformly charged disc of radius R having surface charge density $$\sigma$$ is placed in the xy plane with its center at the origin. Find the electric field intensity along the z-axis at a distance Z from origin :- | [{"identifier": "A", "content": "$$E = {\\sigma \\over {2{\\varepsilon _0}}}\\left( {1 - {Z \\over {{{({Z^2} + {R^2})}^{1/2}}}}} \\right)$$"}, {"identifier": "B", "content": "$$E = {\\sigma \\over {2{\\varepsilon _0}}}\\left( {1 + {Z \\over {{{({Z^2} + {R^2})}^{1/2}}}}} \\right)$$"}, {"identifier": "C", "content": "$... | ["A"] | null | Consider a small ring of radius r and thickness dr on disc.<br><br><img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266111/exam_images/bowbou8oq94cjbuq8clm.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 27th August Morning Shift Physi... | mcq | jee-main-2021-online-27th-august-morning-shift | 10,742 |
1ktfnmd2a | physics | electrostatics | electric-field-and-electric-field-intensity | Figure shows a rod AB, which is bent in a 120$$^\circ$$ circular arc of radius R. A charge ($$-$$Q) is uniformly distributed over rod AB. What is the electric field $$\overrightarrow E $$ at the centre of curvature O ?<br/><br/><img src="data:image/png;base64,UklGRu4OAABXRUJQVlA4IOIOAAAwTwCdASoEAfcAPm02l0ikIyIhIZJ6uIAN... | [{"identifier": "A", "content": "$${{3\\sqrt 3 Q} \\over {8\\pi {\\varepsilon _0}{R^2}}}(\\widehat i)$$"}, {"identifier": "B", "content": "$${{3\\sqrt 3 Q} \\over {8{\\pi ^2}{\\varepsilon _0}{R^2}}}(\\widehat i)$$"}, {"identifier": "C", "content": "$${{3\\sqrt 3 Q} \\over {16{\\pi ^2}{\\varepsilon _0}{R^2}}}(\\widehat ... | ["B"] | null | $$\varepsilon = {{2k\lambda } \over R}\sin \left( {{\theta \over 2}} \right)( - \widehat i)$$<br><br>$$\lambda = \left( {{{ - Q} \over {R\theta }}} \right) = \left( {{{ - Q} \over {R.{{2\pi } \over 3}}}} \right)$$<br><br>$$\lambda = {{ - 3Q} \over {2\pi R}}$$<br><br>$$\varepsilon = {{2k} \over R}.{{ - 3Q} \over {2... | mcq | jee-main-2021-online-27th-august-evening-shift | 10,743 |
1kth0z8vs | physics | electrostatics | electric-field-and-electric-field-intensity | Two particles A and B having charges 20$$\mu$$C and $$-$$5$$\mu$$C respectively are held fixed with a separation of 5 cm. At what position a third charged particle should be placed so that it does not experience a net electric force?<br/><br/><img src="data:image/png;base64,UklGRj4GAABXRUJQVlA4IDIGAABwKACdASoqAUoAPm0yl... | [{"identifier": "A", "content": "At 5 cm from 20 $$\\mu$$C on the left side of system"}, {"identifier": "B", "content": "At 5 cm from $$-$$5 $$\\mu$$C on the right side"}, {"identifier": "C", "content": "At 1.25 cm from $$-$$5 $$\\mu$$C between two charges"}, {"identifier": "D", "content": "At midpoint between two char... | ["B"] | null | Null point is possible only right side of $$-$$5 $$\mu$$C<br><br><img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266442/exam_images/g9xnoxponbufydaqyetl.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 31st August Morning Shift Physics... | mcq | jee-main-2021-online-31st-august-morning-shift | 10,744 |
1l547q70t | physics | electrostatics | electric-field-and-electric-field-intensity | <p>A positive charge particle of 100 mg is thrown in opposite direction to a uniform electric field of strength 1 $$\times$$ 10<sup>5</sup> NC<sup>$$-$$1</sup>. If the charge on the particle is 40 $$\mu$$C and the initial velocity is 200 ms<sup>$$-$$1</sup>, how much distance it will travel before coming to the rest mo... | [{"identifier": "A", "content": "1 m"}, {"identifier": "B", "content": "5 m"}, {"identifier": "C", "content": "10 m"}, {"identifier": "D", "content": "0.5 m"}] | ["D"] | null | <p>$${v^2} - {u^2} = 2as$$</p>
<p>$$ \Rightarrow {0^2} - {200^2} = 2\left( {{{ - qE} \over m}} \right)(S)$$</p>
<p>$$ \Rightarrow - {200^2} = 2\left[ {{{ - 40 \times {{10}^{ - 6}} \times {{10}^5}} \over {100 \times {{10}^{ - 6}}}}} \right][S]$$</p>
<p>$$ \Rightarrow S = {4 \over {2 \times 4}}$$ m = 0.5 m</p> | mcq | jee-main-2022-online-29th-june-morning-shift | 10,745 |
1l55k3s6k | physics | electrostatics | electric-field-and-electric-field-intensity | <p>Two point charges A and B of magnitude +8 $$\times$$ 10<sup>$$-$$6</sup> C and $$-$$8 $$\times$$ 10<sup>$$-$$6</sup> C respectively are placed at a distance d apart. The electric field at the middle point O between the charges is 6.4 $$\times$$ 10<sup>4</sup> NC<sup>$$-$$1</sup>. The distance 'd' between the point c... | [{"identifier": "A", "content": "2.0 m"}, {"identifier": "B", "content": "3.0 m"}, {"identifier": "C", "content": "1.0 m"}, {"identifier": "D", "content": "4.0 m"}] | ["B"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l5hwhjpc/e4eb5f33-6b70-496e-b551-33898f5bfaaa/12008710-01bb-11ed-85a8-43d162d2b7e8/file-1l5hwhjpd.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l5hwhjpc/e4eb5f33-6b70-496e-b551-33898f5bfaaa/12008710-01bb-11ed-85a8-43d162d2b7e8... | mcq | jee-main-2022-online-28th-june-evening-shift | 10,746 |
1l5696143 | physics | electrostatics | electric-field-and-electric-field-intensity | <p>Given below are two statements :</p>
<p>Statement I : A point charge is brought in an electric field. The value of electric field at a point near to the charge may increase if the charge is positive.</p>
<p>Statement II : An electric dipole is placed in a non-uniform electric field. The net electric force on the dip... | [{"identifier": "A", "content": "Both Statement I and Statement II are true."}, {"identifier": "B", "content": "Both Statement I and Statement II are false."}, {"identifier": "C", "content": "Statement I is true but Statement II is false."}, {"identifier": "D", "content": "Statement I is false but Statement II is true.... | ["A"] | null | <p>As one moves closer to a positive charge (isolated) the density of electric field line increases and so does the electric field intensity</p>
<p>$$\Rightarrow$$ Statement I is true</p>
<p>As opposite poles of an electric dipole would experience equal and opposite forces so net force on a dipole in a uniform electric... | mcq | jee-main-2022-online-28th-june-morning-shift | 10,747 |
1l5akfv2q | physics | electrostatics | electric-field-and-electric-field-intensity | <p>In the figure, a very large plane sheet of positive charge is shown. P<sub>1</sub> and P<sub>2</sub> are two points at distance l and 2l from the charge distribution. If $$\sigma$$ is the surface charge density, then the magnitude of electric fields E<sub>1</sub> and E<sub>2</sub> at P<sub>1</sub> and P<sub>2</sub> ... | [{"identifier": "A", "content": "$${E_1} = \\sigma /{\\varepsilon _0},\\,{E_2} = \\sigma /2{\\varepsilon _0}$$"}, {"identifier": "B", "content": "$${E_1} = 2\\sigma /{\\varepsilon _0},\\,{E_2} = \\sigma /{\\varepsilon _0}$$"}, {"identifier": "C", "content": "$${E_1} = {E_2} = \\sigma /2{\\varepsilon _0}$$"}, {"identifi... | ["C"] | null | <p>For an infinite charged plane</p>
<p>$$E = {\sigma \over {2{\varepsilon _0}}}$$ for any value of l</p>
<p>$$ \Rightarrow {E_1} = {E_2} = {\sigma \over {2{\varepsilon _0}}}$$</p> | mcq | jee-main-2022-online-25th-june-morning-shift | 10,749 |
1l5c30ewz | physics | electrostatics | electric-field-and-electric-field-intensity | <p>A vertical electric field of magnitude 4.9 $$\times$$ 10<sup>5</sup> N/C just prevents a water droplet of a mass 0.1 g from falling. The value of charge on the droplet will be :</p>
<p>(Given : g = 9.8 m/s<sup>2</sup>)</p> | [{"identifier": "A", "content": "1.6 $$\\times$$ 10<sup>$$-$$9</sup> C"}, {"identifier": "B", "content": "2.0 $$\\times$$ 10<sup>$$-$$9</sup> C"}, {"identifier": "C", "content": "3.2 $$\\times$$ 10<sup>$$-$$9</sup> C"}, {"identifier": "D", "content": "0.5 $$\\times$$ 10<sup>$$-$$9</sup> C"}] | ["B"] | null | <p>Since the droplet is at rest</p>
<p>$$\Rightarrow$$ Net force = 0</p>
<p>$$\Rightarrow$$ mg = qE</p>
<p>$$\Rightarrow$$ $$q = {{mg} \over E}$$ = 2 $$\times$$ 10<sup>$$-$$9</sup> C</p> | mcq | jee-main-2022-online-24th-june-morning-shift | 10,750 |
1l6i0h93e | physics | electrostatics | electric-field-and-electric-field-intensity | <p>Two uniformly charged spherical conductors $$A$$ and $$B$$ of radii $$5 \mathrm{~mm}$$ and $$10 \mathrm{~mm}$$ are separated by a distance of $$2 \mathrm{~cm}$$. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surface of the ... | [{"identifier": "A", "content": "1 : 2"}, {"identifier": "B", "content": "2 : 1"}, {"identifier": "C", "content": "1 : 1"}, {"identifier": "D", "content": "1 : 4"}] | ["B"] | null | <p>After connection</p>
<p>$${\sigma _1}{R_1} = {\sigma _2}{R_2}$$</p>
<p>Now $$E = {\sigma \over {{\varepsilon _0}}}$$</p>
<p>$$ \Rightarrow {{{E_1}} \over {{E_2}}} = {{{\sigma _1}} \over {{\sigma _2}}} = {{{R_2}} \over {{R_1}}} = {2 \over 1}$$</p> | mcq | jee-main-2022-online-26th-july-evening-shift | 10,751 |
1l6jjbndy | physics | electrostatics | electric-field-and-electric-field-intensity | <p>A long cylindrical volume contains a uniformly distributed charge of density $$\rho \,\mathrm{Cm}^{-3}$$. The electric field inside the cylindrical volume at a distance $$x=\frac{2 \varepsilon_{0}}{\rho} \mathrm{m}$$ from its axis is ________ $$\mathrm{Vm}^{-1}$$.</p>
<p><img src="data:image/png;base64,UklGRmQLAABXR... | [] | null | 1 | <p>$$E = {{\rho r} \over {2{\varepsilon _0}}}$$</p>
<p>at $$r = {{2{\varepsilon _0}} \over \rho }$$</p>
<p>$$E = {\rho \over {2{\varepsilon _0}}}\left( {{{2{\varepsilon _0}} \over \rho }} \right)$$</p>
<p>$$ = 1$$</p> | integer | jee-main-2022-online-27th-july-morning-shift | 10,752 |
1l6nrpc4r | physics | electrostatics | electric-field-and-electric-field-intensity | <p>A uniform electric field $$\mathrm{E}=(8 \mathrm{~m} / \mathrm{e}) \,\mathrm{V} / \mathrm{m}$$ is created between two parallel plates of length $$1 \mathrm{~m}$$ as shown in figure, (where $$\mathrm{m}=$$ mass of electron and e = charge of electron). An electron enters the field symmetrically between the plates with... | [{"identifier": "A", "content": "$$\n\\tan ^{-1}(4)\n$$"}, {"identifier": "B", "content": "$$\n\\tan ^{-1}(2)\n$$"}, {"identifier": "C", "content": "$$\\tan ^{-1}\\left(\\frac{1}{3}\\right)$$"}, {"identifier": "D", "content": "$$\\tan ^{-1}(3)$$"}] | ["B"] | null | <p>$$E = {{8\,m} \over e}$$ V/m</p>
<p>$$l = 1$$ m</p>
<p>$${v_x} = 2$$ m/s</p>
<p>$${a_y} = - 8$$ m/s<sup>2</sup></p>
<p>$$t = {l \over {{v_x}}} = {1 \over 2}s$$</p>
<p>$$ \Rightarrow |{v_y}| = 4$$ m/s</p>
<p>$$\Rightarrow$$ angle of deviation = $$\theta$$</p>
<p>$$\tan \theta = {{{v_y}} \over {{v_x}}}$$</p>
<p>$$\t... | mcq | jee-main-2022-online-28th-july-evening-shift | 10,753 |
1ldoevdjz | physics | electrostatics | electric-field-and-electric-field-intensity | <p>Let $$\sigma$$ be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different region $$E_{I}, E_{I I}$$ and $$E_{I I I}$$ are:</p>
<p><img src="data:image/png;base64,UklGRmQOAABXRUJQVlA4IFgOAABQ4gCdASprAgADP4G+12W2LywnIbFZSsAwCWlu/GPYv4pnZ1+fsH/of... | [{"identifier": "A", "content": "$$\\vec{E}_{I}=0, \\vec{E}_{I I}=\\frac{\\sigma}{\\epsilon_{0}} \\hat{n}, E_{I I I}=0$$"}, {"identifier": "B", "content": "$$\\vec{E}_{I}=\\frac{\\sigma}{2 \\epsilon_{0}} \\hat{n}, \\vec{E}_{I I}=0, \\vec{E}_{I I I}=\\frac{\\sigma}{2 \\epsilon_{0}} \\hat{n}$$"}, {"identifier": "C", "con... | ["C"] | null | Assuming RHS to be $\hat{n}$
<br/><br/>$$
\begin{aligned}
& \vec{E}_{\mathrm{I}}=\frac{\sigma}{2 \epsilon_0}(-\hat{n})+\frac{\sigma}{2 \epsilon_0}(-\hat{n})=-\frac{\sigma}{\epsilon_0} \hat{n} \\\\
& \vec{E}_{I I}=0, \\\\
& \vec{E}_{I I I}=\frac{\sigma}{2 \epsilon_0}(\hat{n})+\frac{\sigma}{2 \epsilon_0}(\hat{n})=\frac{\... | mcq | jee-main-2023-online-1st-february-morning-shift | 10,754 |
1ldognhgi | physics | electrostatics | electric-field-and-electric-field-intensity | <p>Two equal positive point charges are separated by a distance $$2 a$$. The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge $$\mathrm{q}_{0}$$ becomes maximum is $$\frac{a}{\sqrt{x}}$$. The value of $$x$$ is... | [] | null | 2 | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1le7bzmtq/c9c497e4-0d22-40c1-a9ed-d9d25c205d11/052e76e0-ae19-11ed-89cc-995c981e21dd/file-1le7bzmtr.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1le7bzmtq/c9c497e4-0d22-40c1-a9ed-d9d25c205d11/052e76e0-ae19-11ed-89cc-995c981e21dd/fi... | integer | jee-main-2023-online-1st-february-morning-shift | 10,755 |
ldqvo01o | physics | electrostatics | electric-field-and-electric-field-intensity | As shown in the figure, a point charge $Q$ is placed at the centre of conducting spherical shell of inner radius $a$ and outer radius $b$. The electric field due to charge $\mathrm{Q}$ in three different regions $\mathrm{I}, \mathrm{II}$ and $\mathrm{III}$ is given by:<br/><br/>
$(\mathrm{I}: r < a, \mathrm{II}: a &... | [{"identifier": "A", "content": "$E_I=0, E_{I I}=0, E_{I I I} \\neq 0$"}, {"identifier": "B", "content": "$E_I \\neq 0, E_{I I}=0, E_{III}=0$"}, {"identifier": "C", "content": "$E_I \\neq 0, E_{I I}=0, E_{III} \\neq 0$"}, {"identifier": "D", "content": "$E_I=0, E_{I I}=0, E_{I I I}=0$"}] | ["C"] | null | <p>$${E_I} \ne 0$$ (inside region)</p>
<p>$${E_{II}} = 0$$ (conducting region)</p>
<p>$${E_{III}} \ne 0$$</p>
<p>$$ = {{KQ} \over {{r^2}}}\,\,\,(r > b)$$</p> | mcq | jee-main-2023-online-30th-january-evening-shift | 10,756 |
1ldr1dwex | physics | electrostatics | electric-field-and-electric-field-intensity | <p>Electric field in a certain region is given by $$\overrightarrow{\mathrm{E}}=\left(\frac{\mathrm{A}}{x^{2}} \hat{i}+\frac{\mathrm{B}}{y^{3}} \hat{j}\right) \text {. The } \mathrm{SI} \text { unit of } \mathrm{A} \text { and } \mathrm{B}$$ are :</p> | [{"identifier": "A", "content": "$$\\mathrm{Nm}^{2} \\mathrm{C} ; \\mathrm{Nm}^{3} \\mathrm{C}$$"}, {"identifier": "B", "content": "$$\\mathrm{Nm}^{3} \\mathrm{C}^{-1} ; \\mathrm{Nm}^{2} \\mathrm{C}^{-1}$$"}, {"identifier": "C", "content": "$$\\mathrm{Nm}^{3} \\mathrm{C} ; \\mathrm{Nm}^{2} \\mathrm{C}$$"}, {"identifier... | ["D"] | null | <p>$$\overrightarrow E = \left( {{A \over {{x^2}}}\widehat i + {B \over {{y^3}}}\widehat j} \right)$$</p>
<p>$$\left[ {{A \over {{x^2}}}} \right] = [E] = \left[ {{F \over q}} \right] = \left[ {{N \over C}} \right] = N{C^{ - 1}}$$</p>
<p>$$\mathrm{[A] = (N{m^2}{C^{ - 1}})}$$</p>
<p>$$\mathrm{[B] = N{m^3}{C^{ - 1}}}$$</... | mcq | jee-main-2023-online-30th-january-morning-shift | 10,757 |
1ldsb78kq | physics | electrostatics | electric-field-and-electric-field-intensity | <p>A point charge $$2\times10^{-2}~\mathrm{C}$$ is moved from P to S in a uniform electric field of $$30~\mathrm{NC^{-1}}$$ directed along positive x-axis. If coordinates of P and S are (1, 2, 0) m and (0, 0, 0) m respectively, the work done by electric field will be</p> | [{"identifier": "A", "content": "600 mJ"}, {"identifier": "B", "content": "$$-1200$$ mJ"}, {"identifier": "C", "content": "1200 mJ"}, {"identifier": "D", "content": "$$-600$$ mJ"}] | ["D"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1let3h9fn/25ba725f-606b-445d-8cf6-b491ca398815/fb86c530-ba10-11ed-bf62-29125e0e0d77/file-1let3h9fo.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1let3h9fn/25ba725f-606b-445d-8cf6-b491ca398815/fb86c530-ba10-11ed-bf62-29125e0e0d77... | mcq | jee-main-2023-online-29th-january-evening-shift | 10,758 |
1ldtyr0m1 | physics | electrostatics | electric-field-and-electric-field-intensity | <p>A point charge of 10 $$\mu$$C is placed at the origin. At what location on the X-axis should a point charge of 40 $$\mu$$C be placed so that the net electric field is zero at $$x=2$$cm on the X-axis?</p> | [{"identifier": "A", "content": "$$x=6$$ cm"}, {"identifier": "B", "content": "$$x=8$$ cm"}, {"identifier": "C", "content": "$$x=4$$ cm"}, {"identifier": "D", "content": "$$x=-4$$ cm"}] | ["A"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1ledkim7h/2a5846c1-6725-40f5-a507-26fbada88443/1201c2c0-b187-11ed-8feb-a5a20e534682/file-1ledkim7l.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1ledkim7h/2a5846c1-6725-40f5-a507-26fbada88443/1201c2c0-b187-11ed-8feb-a5a20e534682... | mcq | jee-main-2023-online-25th-january-evening-shift | 10,759 |
1ldujsxo5 | physics | electrostatics | electric-field-and-electric-field-intensity | <p>A uniform electric field of 10 N/C is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy 0.5 eV. The length of each plate is 10 cm. The angle ($$\theta$$) of deviation of the path of electron as it comes out of the fie... | [] | null | 45 | $$
\begin{aligned}
& 0.5 \mathrm{e}=\frac{1}{2} \mathrm{mv}_{\mathrm{x}}^2 \Rightarrow \mathrm{v}_{\mathrm{x}}=\sqrt{\frac{\mathrm{e}}{\mathrm{m}}} \\\\
& \text { Along } \mathrm{x} \mathrm{L}=\mathrm{v}_{\mathrm{x}} \mathrm{t}=\sqrt{\frac{\mathrm{e}}{\mathrm{m}}} \mathrm{t} \\\\
& \text { Along y } \mathrm{v}_{\mathrm... | integer | jee-main-2023-online-25th-january-morning-shift | 10,760 |
1ldyf57yt | physics | electrostatics | electric-field-and-electric-field-intensity | <p>A stream of a positively charged particles having $${q \over m} = 2 \times {10^{11}}{C \over {kg}}$$ and velocity $${\overrightarrow v _0} = 3 \times {10^7}\widehat i\,m/s$$ is deflected by an electric field $$1.8\widehat j$$ kV/m. The electric field exists in a region of 10 cm along $$x$$ direction. Due to the elec... | [] | null | 2 | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1le1lduvl/ce1453ce-9f24-417e-b0cb-3f2d000af47e/0efec010-aaf1-11ed-9454-6baf9e2c8206/file-1le1lduvm.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1le1lduvl/ce1453ce-9f24-417e-b0cb-3f2d000af47e/0efec010-aaf1-11ed-9454-6baf9e2c8206/fi... | integer | jee-main-2023-online-24th-january-morning-shift | 10,761 |
lgnxxzq9 | physics | electrostatics | electric-field-and-electric-field-intensity | The electric field due to a short electric dipole at a large distance $(r)$ from center of dipole on the equatorial plane varies with distance as : | [{"identifier": "A", "content": "$\\frac{1}{r^{2}}$"}, {"identifier": "B", "content": "$\\frac{1}{r}$"}, {"identifier": "C", "content": "$r$"}, {"identifier": "D", "content": "$\\frac{1}{r^{3}}$"}] | ["D"] | null | At a large distance $r$ from the center of a short electric dipole, the electric field on the equatorial plane can be approximated as:
<br/><br/>
$$
E = \frac{1}{4\pi\epsilon_0}\frac{2p}{r^3}
$$
<br/><br/>
where $p$ is the dipole moment of the electric dipole, and $\epsilon_0$ is the permittivity of free space.
<br/><b... | mcq | jee-main-2023-online-15th-april-morning-shift | 10,762 |
1lgq3kzim | physics | electrostatics | electric-field-and-electric-field-intensity | <p>A thin infinite sheet charge and an infinite line charge of respective charge densities $$+\sigma$$ and $$+\lambda$$ are placed parallel at $$5 \mathrm{~m}$$ distance from each other. Points 'P' and 'Q' are at $$\frac{3}{\pi}$$ m and $$\frac{4}{\pi}$$ m perpendicular distances from line charge towards sheet charge, ... | [] | null | 6 | With the given equations:
<br/><br/>
$$E_P = \left|\frac{\sigma}{2 \varepsilon_0} - \frac{1}{4 \pi \varepsilon_0} \frac{2 \lambda}{3 / \pi}\right| = \left|\frac{\sigma}{2 \varepsilon_0} - \frac{\lambda}{6 \varepsilon_0}\right| = \frac{\sigma}{6 \varepsilon_0}$$
<br/><br/>
$$E_Q = \left|\frac{\sigma}{2 \varepsilon_0} - ... | integer | jee-main-2023-online-13th-april-morning-shift | 10,763 |
1lgvraetn | physics | electrostatics | electric-field-and-electric-field-intensity | <p>In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor</p> | [{"identifier": "A", "content": "move in the straight line paths in the same direction"}, {"identifier": "B", "content": "move with the uniform velocity throughout from lower potential to higher potential"}, {"identifier": "C", "content": "drift from higher potential to lower potential."}, {"identifier": "D", "content"... | ["D"] | null | Electron drifts from lower potential to higher potential on curved path. | mcq | jee-main-2023-online-10th-april-evening-shift | 10,764 |
1lgvtfi9a | physics | electrostatics | electric-field-and-electric-field-intensity | <p>An electron revolves around an infinite cylindrical wire having uniform linear charge density $$2 \times 10^{-8} \mathrm{C} \mathrm{m}^{-1}$$ in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of electron with which it is revolving is ___________ $$\times 10^{... | [] | null | 8 | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1lib9p35q/8dd86071-ea0f-467e-a896-508012037767/0dc0c5e0-ff74-11ed-9ba6-21b4d8b62881/file-1lib9p35r.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1lib9p35q/8dd86071-ea0f-467e-a896-508012037767/0dc0c5e0-ff74-11ed-9ba6-21b4d8b62881/fi... | integer | jee-main-2023-online-10th-april-evening-shift | 10,765 |
1lh00znbo | physics | electrostatics | electric-field-and-electric-field-intensity | <p>Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius $$\mathrm{R}$$, with distance $$r$$ from the centre O is represented by:</p>
<p><img src="data:image/png;base64,UklGRmAQAABXRUJQVlA4IFQQAADQKQGdASrxAgADP4HA32U2Mi+nInUI6sAwCWlu4XBlEmNwvHR0gNOZ93/5j/+8DKfDuX8/XRQRPVf/Rg... | [{"identifier": "A", "content": "<img src=\"https://app-content.cdn.examgoal.net/fly/@width/image/1lh1hewlr/83904e3a-2ce3-4a84-9e4d-16df6596ef90/2dc38180-e646-11ed-9b1f-cf98cc51cb3d/file-1lh1hewm0.png?format=png\" data-orsrc=\"https://app-content.cdn.examgoal.net/image/1lh1hewlr/83904e3a-2ce3-4a84-9e4d-16df6596ef90/2dc... | ["D"] | null | Electric field due to the uniformly charged solid sphere is given by<br><br>
$$
\begin{array}{ll}
\mathrm{E}=\frac{\mathrm{Q}}{4 \pi \varepsilon_0 r^2} \quad r \geq \mathrm{R} \\\\
\& & \\\\
\mathrm{E}=\frac{\mathrm{Q} r}{4 \pi \varepsilon_0 \mathrm{R}^3} \quad r \leq \mathrm{R}
\end{array}
$$<br><br>
Therefore... | mcq | jee-main-2023-online-8th-april-morning-shift | 10,766 |
lsancm3c | physics | electrostatics | electric-field-and-electric-field-intensity | Suppose a uniformly charged wall provides a uniform electric field of $2 \times 10^4 \mathrm{~N} / \mathrm{C}$ normally. A charged particle of mass $2 \mathrm{~g}$ being suspended through a silk thread of length $20 \mathrm{~cm}$ and remain stayed at a distance of $10 \mathrm{~cm}$ from the wall. <br/><br/>Then the cha... | [] | null | 3 | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lsc0tkq8/ba672f20-8640-4879-9e31-ae8d9fb385cc/4ad67300-c5d8-11ee-baf2-61ef5327b65c/file-6y3zli1lsc0tkq9.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/6y3zli1lsc0tkq8/ba672f20-8640-4879-9e31-ae8d9fb385cc/4ad67300-c5d8-11ee-ba... | integer | jee-main-2024-online-1st-february-evening-shift | 10,767 |
jaoe38c1lscpi6ha | physics | electrostatics | electric-field-and-electric-field-intensity | <p>Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).</p>
<p>Assertion (A) : Work done by electric field on moving a positive charge on an equipotential surface is always zero.</p>
<p>Reason (R) : Electric lines of forces are always perpendicular to equipotential ... | [{"identifier": "A", "content": "Both (A) and (R) are correct and (R) is the correct explanation of (A)\n"}, {"identifier": "B", "content": "(A) is correct but (R) is not correct\n"}, {"identifier": "C", "content": "Both (A) and (R) are correct but (R) is not the correct explanation of (A)\n"}, {"identifier": "D", "con... | ["A"] | null | <p>The most appropriate answer from the options given would be Option A: Both (A) and (R) are correct, and (R) is the correct explanation of (A).</p>
<p>Here is the reasoning for this answer:</p>
<p>Assertion (A) states that the work done by an electric field on moving a positive charge on an equipotential surface is a... | mcq | jee-main-2024-online-27th-january-evening-shift | 10,768 |
jaoe38c1lse6341e | physics | electrostatics | electric-field-and-electric-field-intensity | <p>Two charges $$q$$ and $$3 q$$ are separated by a distance '$$r$$' in air. At a distance $$x$$ from charge $$q$$, the resultant electric field is zero. The value of $$x$$ is :</p> | [{"identifier": "A", "content": "$$\\frac{r}{3(1+\\sqrt{3})}$$\n"}, {"identifier": "B", "content": "$$\\frac{(1+\\sqrt{3})}{r}$$\n"}, {"identifier": "C", "content": "$$\\frac{r}{(1+\\sqrt{3})}$$\n"}, {"identifier": "D", "content": "$$r(1+\\sqrt{3})$$"}] | ["C"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lsluewb7/95253c3b-95ab-4fdb-8ed5-a7454583f0ab/125df630-cb3f-11ee-ad47-a16d1086e690/file-6y3zli1lsluewb8.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/6y3zli1lsluewb7/95253c3b-95ab-4fdb-8ed5-a7454583f0ab/125df630-cb3f-11ee... | mcq | jee-main-2024-online-31st-january-morning-shift | 10,769 |
jaoe38c1lsf24sv2 | physics | electrostatics | electric-field-and-electric-field-intensity | <p>An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet $$\mathrm{S}$$ having surface charge density $$+\sigma$$. The electron at $$t=0$$ is at a distance of $$1 \mathrm{~m}$$ from $$S$$ and has a speed of $$1 \mathrm{~m} / \mathrm{s}$$. The maximum value of $$\sig... | [] | null | 8 | <p>$$\begin{aligned}
& \mathrm{u}=1 \mathrm{~m} / \mathrm{s} ; \mathrm{a}=-\frac{\sigma \mathrm{e}}{2 \varepsilon_0 \mathrm{~m}} \\
& \mathrm{t}=1 \mathrm{~s} \\
& \mathrm{~S}=-1 \mathrm{~m} \\
& \text { Using } \mathrm{S}=\mathrm{ut}+\frac{1}{2} \mathrm{at}^2 \\
& -1=1 \times 1-\frac{1}{2} \times \frac{\sigma \mathrm{... | integer | jee-main-2024-online-29th-january-morning-shift | 10,770 |
lv0vy04k | physics | electrostatics | electric-field-and-electric-field-intensity | <p>An infinite plane sheet of charge having uniform surface charge density $$+\sigma_{\mathrm{s}} \mathrm{C} / \mathrm{m}^2$$ is placed on $$x$$-$$y$$ plane. Another infinitely long line charge having uniform linear charge density $$+\lambda_e \mathrm{C} / \mathrm{m}$$ is placed at $$z=4 \mathrm{~m}$$ plane and paralle... | [] | null | 16 | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1lwke0sgr/0bf030fe-5b9f-41bd-b2d3-b2c46d13c08d/0cde17a0-19a3-11ef-affc-a9250ab93b8d/file-1lwke0sgs.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1lwke0sgr/0bf030fe-5b9f-41bd-b2d3-b2c46d13c08d/0cde17a0-19a3-11ef-affc-a9250ab93b8d... | integer | jee-main-2024-online-4th-april-morning-shift | 10,771 |
lv3vegm2 | physics | electrostatics | electric-field-and-electric-field-intensity | <p>If the net electric field at point $$\mathrm{P}$$ along $$\mathrm{Y}$$ axis is zero, then the ratio of $$\left|\frac{q_2}{q_3}\right|$$ is $$\frac{8}{5 \sqrt{x}}$$, where $$x=$$ ________.</p>
<p><img src="data:image/png;base64,UklGRvIMAABXRUJQVlA4IOYMAAAQ0ACdASoAAyICP4HA3WU2Mi4nInS46sAwCWlu/Eb4+VEHZ1+frl/v+uD5l2fLaD... | [] | null | 5 | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1lw4zambw/bfdb46d1-98c0-46b0-bfe1-e5f51fd784cf/b38abcc0-1129-11ef-94b0-47c9adc12525/file-1lw4zambx.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1lw4zambw/bfdb46d1-98c0-46b0-bfe1-e5f51fd784cf/b38abcc0-1129-11ef-94b0-47c9adc12525... | integer | jee-main-2024-online-8th-april-evening-shift | 10,772 |
lvc58eje | physics | electrostatics | electric-field-and-electric-field-intensity | <p>Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point $$P$$ is $$\frac{x \sigma}{\epsilon_0}$$. The value of $$x$$ is _________ (all quantities are measured in SI units).</p>
<p><img src="data:image/png;base64,UklGRhoKAABXRUJQVlA4IA4KAAAwoQCdASoAA+sBP4G... | [] | null | 2 | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1lvbygqyi/370ba3d5-f8dd-40fb-a02a-62c93ee724fb/ba02a4b0-0133-11ef-a1be-0551bbcf7858/file-1lvbygqyj.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1lvbygqyi/370ba3d5-f8dd-40fb-a02a-62c93ee724fb/ba02a4b0-0133-11ef-a1be-0551bbcf7858/fi... | integer | jee-main-2024-online-6th-april-morning-shift | 10,773 |
AdlQan0IvxBgIdHW | physics | electrostatics | electric-flux-and-gauss-law | The region between two concentric spheres of radii $$'a'$$ and $$'b',$$ respectively (see figure), have volume charge density $$\rho = {A \over r},$$ where $$A$$ is a constant and $$r$$ is the distance from the center. A such that the electric field in the region between the spheres will be constant, is : <br/><br/>
<... | [{"identifier": "A", "content": "$${{2Q} \\over {\\pi \\left( {{a^2} - {b^2}} \\right)}}$$ "}, {"identifier": "B", "content": "$${{2Q} \\over {\\pi \\,{a^2}}}$$ "}, {"identifier": "C", "content": "$${Q \\over {2\\pi \\,{a^2}}}$$ "}, {"identifier": "D", "content": "$${Q \\over {2\\pi \\,\\left( {{b^2} - {a^2}} \\right)}... | ["C"] | null | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l7zdkk3b/787cd411-da4c-4be6-9f4e-fa3cd1ce4d2b/a2b8dc70-32ef-11ed-8cf6-c1445513adbd/file-1l7zdkk3c.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l7zdkk3b/787cd411-da4c-4be6-9f4e-fa3cd1ce4d2b/a2b8dc70-32ef-11ed-8cf6-c1445513adbd/fi... | mcq | jee-main-2016-offline | 10,776 |
Fn7QXCr9RP6J2k9MBu6A1 | physics | electrostatics | electric-flux-and-gauss-law | Four closed surfaces and corresponding charge distributions are shown below.
<br/><br/><img src="data:image/png;base64,UklGRsgcAABXRUJQVlA4ILwcAACQGgGdASoAAzMCP4G+2GU2MCynIjLpgsAwCWlu/GKv6ZH0Uu9M8bevzx/te4naAL//w25u7MeAdkh2RYBvj/9ludD97shp5z/58HT/1+nQJw110a6v+cGT84Mn5two8WIy8Td4Ec3GvkJrERaarl/jZ9ANvfOxAZ77xijnrgmKZwZPy... | [{"identifier": "A", "content": "$${\\Phi _1}$$ < $${\\Phi _2}$$ = $${\\Phi _3}$$ > $${\\Phi _4}$$"}, {"identifier": "B", "content": "$${\\Phi _1}$$ > $${\\Phi _2}$$ > $${\\Phi _3}$$ > $${\\Phi _4}$$"}, {"identifier": "C", "content": "$${\\Phi _1}$$ = $${\\Phi _2}$$ = $${\\Phi _3}$$ = $${\\Phi _4}$... | ["C"] | null | Net flux through a closed surface,
<br><br>$$\phi $$ = $${{{q_{enclose}}} \over {{\varepsilon _0}}}$$
<br><br>q<sub>enclosed</sub> = charge enclosed by closed surface.
<br><br>For surface S<sub>1</sub>,
<br><br>$$\phi $$<sub>1</sub> = $${1 \over {{\varepsilon _0}}}$$ (2q)
<br><br>For surface S<sub>2</sub>,
<br><br>$$... | mcq | jee-main-2017-online-9th-april-morning-slot | 10,777 |
XH3KjWoVZfPCtcGCDSEPj | physics | electrostatics | electric-flux-and-gauss-law | A charge $$Q$$ is placed at a distance $$a/2$$ above the center of the square surface of edge a as shown in the figure. <br/><br/><img src="data:image/png;base64,UklGRqQNAABXRUJQVlA4IJgNAAAQ+QCdASq8AgADP4HA3GW2MS2nIXEJEsAwCWlu4XET0mNwvVQVgq/1e5z/TrA8d9B59ulw907//+uQimk7sQ7lY92Idyse7ELoX/aeG26PNe+tIQXGDR+edqCC4waPzztGN4... | [{"identifier": "A", "content": "$${Q \\over {{ \\in _0}}}$$ "}, {"identifier": "B", "content": "$${Q \\over {2{ \\in _0}}}$$"}, {"identifier": "C", "content": "$${Q \\over {3{ \\in _0}}}$$"}, {"identifier": "D", "content": "$${Q \\over {6{ \\in _0}}}$$"}] | ["D"] | null | As in a cube there is 6 faces, you can think this surface is one face among 6 faces. If the side of cube is a length then its center will be $${a \over 2}$$ distance from any surface.
<br><br>So, we can assume point charge Q is at the center of the cube and total electric flux due to this charge will pass evently thr... | mcq | jee-main-2018-online-15th-april-morning-slot | 10,778 |
turqbisDNbatgaMbfE7k9k2k5le99nt | physics | electrostatics | electric-flux-and-gauss-law | An electric field $$\overrightarrow E = 4x\widehat i - \left( {{y^2} + 1} \right)\widehat j$$ N/C
<br/>passes through the box shown in figure. The
<br/>flux of the electric field through surfaces ABCD
<br/>and BCGF are marked as $${\phi _I}$$ and $${\phi _{II}}$$
<br/>respectively. The difference between $$\left( {{\p... | [] | null | -48 | Flux via ABCD
<br><br>$$\phi $$<sub>I</sub> = $$\int {\overrightarrow E } .d\overrightarrow A $$ = 0
<br><br>Flux via EFGH
<br><br>$$\phi $$<sub>II</sub> = $$\int {\overrightarrow E } .d\overrightarrow A $$
<br><br>= [$$4x\widehat i - \left( {{y^2} + 1} \right)\widehat j$$].4$$\widehat i$$
<br><br>= 16x = 16 $$ \times ... | integer | jee-main-2020-online-9th-january-evening-slot | 10,781 |
OBKHwWwQQFaeUrKVc01klrp1vk1 | physics | electrostatics | electric-flux-and-gauss-law | A point charge of +12$$\mu$$C is at a distance 6 cm vertically above the centre of a square of side 12 cm as shown in figure. The magnitude of the electric flux through the square will be __________ $$\times$$ 10<sup>3</sup> Nm<sup>2</sup>/C.<br/><br/>
<img src="data:image/png;base64,UklGRrINAABXRUJQVlA4IKYNAABQ8gCdASp... | [] | null | 226 | <p>Given, charge, q = 12 $$\mu$$C = 12 $$\times$$ 10<sup>$$-$$6</sup>C</p><p>Height of charge from surface, h = 6 cm = 6 $$\times$$ 10<sup>$$-$$2</sup> m and side of square, a = 12 cm = 12 $$\times$$ 10<sup>$$-$$2</sup> m</p>
<p>Using Gauss law, it is a part of cube of side 12 cm and charge at centre so;</p><p>$$\phi ... | integer | jee-main-2021-online-24th-february-evening-slot | 10,782 |
JcriDx6teXm9XL4cDa1klrz1rhm | physics | electrostatics | electric-flux-and-gauss-law | The electric field in a region is given by $$\overrightarrow E = \left( {{3 \over 5}{E_0}\widehat i + {4 \over 5}{E_0}\widehat j} \right){N \over C}$$. The ratio of flux of reported field through the rectangular surface of area 0.2 m<sup>2</sup> (parallel to y $$-$$ z plane) to that of the surface of area 0.3 m<sup>2<... | [] | null | 1 | $$\phi = \overrightarrow E \,.\,\overrightarrow A $$<br><br>$${\overrightarrow A _a} = 0.2\widehat i$$<br><br>$${\overrightarrow A _b} = 0.3\widehat j$$<br><br>$${\phi _a} = \left( {{3 \over 5}{E_0}\widehat i + {4 \over 5}{E_0}\widehat j} \right).\,0.2\widehat i$$<br><br>$$ \Rightarrow $$ $${\phi _a} = {3 \over 5}{E_0... | integer | jee-main-2021-online-25th-february-morning-slot | 10,783 |
3h9rsgxff6fwc92zST1klt2rjao | physics | electrostatics | electric-flux-and-gauss-law | A charge 'q' is placed at one corner of a cube as shown in figure. The flux of electrostatic field $$\overrightarrow E $$ through the shaded area is :<br/><br/><img src="data:image/png;base64,UklGRrgLAABXRUJQVlA4IKwLAABQRQCdASooAdsAPm0ylkkkIqIhIpPaMIANiWlu4W/RG/Nj8ZfyD8VfAT+b/h91vPhn2Y22DtgfYP5B/av9r/Y/2v+M/7RwBHp3+1/y... | [{"identifier": "A", "content": "$${q \\over {24{\\varepsilon _0}}}$$"}, {"identifier": "B", "content": "$${q \\over {48{\\varepsilon _0}}}$$"}, {"identifier": "C", "content": "$${q \\over {4{\\varepsilon _0}}}$$"}, {"identifier": "D", "content": "$${q \\over {8{\\varepsilon _0}}}$$"}] | ["A"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266226/exam_images/ii14yqpafwri8ffjkuir.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 25th February Evening Shift Physics - Electrostatics Question 119 English Explanation">
<br>Flux t... | mcq | jee-main-2021-online-25th-february-evening-slot | 10,784 |
At72mgUy4nc2YEMxOn1kmkc7mfk | physics | electrostatics | electric-flux-and-gauss-law | The electric field in a region is given by $$\overrightarrow E = {2 \over 5}{E_0}\widehat i + {3 \over 5}{E_0}\widehat j$$ with $${E_0} = 4.0 \times {10^3}{N \over C}$$. The flux of this field through a rectangular surface area 0.4 m<sup>2</sup> parallel to the Y-Z plane is __________ Nm<sup>2</sup>C<sup>$$-$$1</sup>. | [] | null | 640 | $$\phi = \overrightarrow E \,.\,\overrightarrow A $$<br><br>$$ = {{{E_0}} \over 5}\left( {2\widehat i + 3\widehat j} \right)\,.\,\left( {0.4\widehat i} \right)$$<br><br>$$ = {{4000} \over 5}\left( {2 \times 0.4} \right)$$<br><br>$$ = 640$$ Nm<sup>2</sup> C<sup>$$-$$1</sup> | integer | jee-main-2021-online-17th-march-evening-shift | 10,785 |
1krsxmb0y | physics | electrostatics | electric-flux-and-gauss-law | The total charge enclosed in an incremental volume of 2 $$\times$$ 10<sup>$$-$$9</sup> m<sup>3</sup> located at the origin is ___________ nC, if electric flux density of its field is found as<br/><br/>D = e<sup>$$-$$x</sup> sin y $$\widehat i$$ $$-$$ e<sup>$$-$$x</sup> cos y $$\widehat j$$ + 2z $$\widehat k$$ C/m<sup>2... | [] | null | 4 | $$\overline D = {\varepsilon _0}\overline E $$<br><br>$$Div.\,\overline E = {\rho \over {{\varepsilon _0}}}$$<br><br>$$ \Rightarrow div.\,\overline D = \rho $$<br><br>$$ \Rightarrow {\partial \over {\partial x}}\left( {{e^{ - x}}\sin y} \right) + {\partial \over {\partial y}}\left( { - {e^{ - x}}\cos y} \right) +... | integer | jee-main-2021-online-22th-july-evening-shift | 10,786 |
1ktjpcd4j | physics | electrostatics | electric-flux-and-gauss-law | Choose the incorrect statement :<br/><br/>(1) The electric lines of force entering into a Gaussian surface provide negative flux.<br/><br/>(2) A charge 'q' is placed at the centre of a cube. The flux through all the faces will be the same.<br/><br/>(3) In a uniform electric field net flux through a closed Gaussian surf... | [{"identifier": "A", "content": "(3) and (4) only"}, {"identifier": "B", "content": "(2) and (4) only"}, {"identifier": "C", "content": "(4) only"}, {"identifier": "D", "content": "(1) and (3) only"}] | ["C"] | null | Since, $$\phi = \overrightarrow E \,.\,\overrightarrow A = EA\cos \theta $$<br><br> <picture><source media="(max-width: 320px)" srcset="https://res.cloudinary.com/dckxllbjy/image/upload/v1734263307/exam_images/ko7kc2awilrkhk7vobnx.webp"><source media="(max-width: 500px)" srcset="https://res.cloudinary.com/dckxllbjy/i... | mcq | jee-main-2021-online-31st-august-evening-shift | 10,787 |
1ktmllj80 | physics | electrostatics | electric-flux-and-gauss-law | A cube is placed inside an electric field, $$\overrightarrow E = 150{y^2}\widehat j$$. The side of the cube is 0.5 m and is placed in the field as shown in the given figure. The charge inside the cube is :<br/><br/>
<img src="data:image/png;base64,UklGRqwOAABXRUJQVlA4IKAOAABQrgCdASoAA4EBP4G+2GY2LysnIbEJKsAwCWlu/C44T+t... | [{"identifier": "A", "content": "3.8 $$\\times$$ 10<sup>$$-$$11</sup> C"}, {"identifier": "B", "content": "8.3 $$\\times$$ 10<sup>$$-$$11</sup> C"}, {"identifier": "C", "content": "3.8 $$\\times$$ 10<sup>$$-$$12</sup> C"}, {"identifier": "D", "content": "8.3 $$\\times$$ 10<sup>$$-$$12</sup> C"}] | ["B"] | null | Given, the side of the cube, s = 0.5 m<br><br>Electric field, E = 150 y<sup>2</sup>$$\widehat j$$<br><br>The direction of electric field is as shown in the below figure,<br><br> <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kx8uqi20/9a4ce6c4-cd3e-479e-a207-e988f9dc7cbc/6fe05680-5e5f-11ec-b90f-db93470... | mcq | jee-main-2021-online-1st-september-evening-shift | 10,788 |
1l56uxasq | physics | electrostatics | electric-flux-and-gauss-law | <p>If a charge q is placed at the centre of a closed hemispherical non-conducting surface, the total flux passing through the flat surface would be :</p>
<p> <img src="data:image/png;base64,UklGRlgZAABXRUJQVlA4IEwZAABQXAGdASoAA+EBP4G+12I2MTimJTPKMxAwCWlu/ExXtO/e3niU3QUvpb/Tf4j9///n82eofqT+HdipjX+7//+5c///6n//99XcDwAvwT... | [{"identifier": "A", "content": "$${q \\over {{ \\in _0}}}$$"}, {"identifier": "B", "content": "$${q \\over {{ 2\\in _0}}}$$"}, {"identifier": "C", "content": "$${q \\over {{ 4\\in _0}}}$$"}, {"identifier": "D", "content": "$${q \\over {{ 2\\pi\\in _0}}}$$"}] | ["B"] | null | <p>Flux passing through flat surface = Flux passing through curved surface.</p>
<p>So, $$\phi = {q \over {2{\varepsilon _0}}}$$</p> | mcq | jee-main-2022-online-27th-june-evening-shift | 10,789 |
1l6p4vott | physics | electrostatics | electric-flux-and-gauss-law | <p>A spherically symmetric charge distribution is considered with charge density varying as</p>
<p>$$\rho(r)= \begin{cases}\rho_{0}\left(\frac{3}{4}-\frac{r}{R}\right) & \text { for } r \leq R \\ \text { zero } & \text { for } r>R\end{cases}$$</p>
<p>Where, $$r(r < R)$$ is the distance from the centre O (... | [{"identifier": "A", "content": "$$\\frac{\\rho_{0} \\mathrm{r}}{4 \\varepsilon_{0}}\\left(\\frac{3}{4}-\\frac{r}{R}\\right)$$"}, {"identifier": "B", "content": "$$\\frac{\\rho_{0} r}{3 \\varepsilon_{0}}\\left(\\frac{3}{4}-\\frac{r}{R}\\right)$$"}, {"identifier": "C", "content": "$$\\frac{\\rho_{0} r}{4 \\varepsilon_{0... | ["C"] | null | <p>$$\left( {4\pi {r^2}} \right){E_\rho } = {{{Q_{in}}} \over {{\varepsilon _0}}}$$</p>
<p>$$ = {{\int_0^r {{\rho _0}\left( {{3 \over 4} - {r \over 4}} \right)4\pi {r^2}dr} } \over {{\varepsilon _0}}}$$</p>
<p>$$ = {{{\rho _0}\pi 4} \over {{\varepsilon _0}}}\left( {{{{r^3}} \over 4} - {{{r^4}} \over {4R}}} \right)$$</p... | mcq | jee-main-2022-online-29th-july-morning-shift | 10,790 |
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