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__index_level_0__
int64
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13.4k
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 &gt;&gt; 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>$$ \therefore $$&nbsp;&nbsp;At P, F $$ = - {{K\overrightarrow P } \over {{r^3}}}$$Q. <br><br>At &nbsp;&nbsp;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 &lt; \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&gt;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 &gt;&gt; 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": "$${1 \\over {4\\pi {\\varepsilon _0}}}{{qQ} \\over {{R^2}}} &gt; F &gt; 0$$ for r &lt; R"}, {"identifier": "B", "content": "$$F = {1 \\over {4\\pi {\\varepsilon _0}}}{{qQ} \\over {{r^2}}}$$ for r &gt; 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 &gt; 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 _ + }$$| &gt; |$${\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 $$ as a function of distance r from centre O is given by <br/><br/><img src="data:image/png;base64,...
[{"identifier": "A", "content": "<img src=\"https://res.cloudinary.com/dckxllbjy/image/upload/v1734265907/exam_images/ungsj8uestkmco5xgnla.webp\" style=\"max-width: 100%;height: auto;display: block;margin: 0 auto;\" loading=\"lazy\" alt=\"JEE Main 2021 (Online) 26th August Morning Shift Physics - Electrostatics Questio...
["A"]
null
Considering outer spherical shell is non-conducting.<br><br>Electric field inside a metal sphere is zero.<br><br>r &lt; R $$\Rightarrow$$ E = 0<br><br>r &gt; R $$\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$$ is...
[]
null
2
<img src="https://app-content.cdn.examgoal.net/fly/@width/image/1le7bzmtq/c9c497e4-0d22-40c1-a9ed-d9d25c205d11/052e76e0-ae19-11ed-89cc-995c981e21dd/file-1le7bzmtr.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1le7bzmtq/c9c497e4-0d22-40c1-a9ed-d9d25c205d11/052e76e0-ae19-11ed-89cc-995c981e21dd/fi...
integer
jee-main-2023-online-1st-february-morning-shift
10,755
ldqvo01o
physics
electrostatics
electric-field-and-electric-field-intensity
As shown in the figure, a point charge $Q$ is placed at the centre of conducting spherical shell of inner radius $a$ and outer radius $b$. The electric field due to charge $\mathrm{Q}$ in three different regions $\mathrm{I}, \mathrm{II}$ and $\mathrm{III}$ is given by:<br/><br/> $(\mathrm{I}: r &lt; a, \mathrm{II}: a &...
[{"identifier": "A", "content": "$E_I=0, E_{I I}=0, E_{I I I} \\neq 0$"}, {"identifier": "B", "content": "$E_I \\neq 0, E_{I I}=0, E_{III}=0$"}, {"identifier": "C", "content": "$E_I \\neq 0, E_{I I}=0, E_{III} \\neq 0$"}, {"identifier": "D", "content": "$E_I=0, E_{I I}=0, E_{I I I}=0$"}]
["C"]
null
<p>$${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> $$ \begin{array}{ll} \mathrm{E}=\frac{\mathrm{Q}}{4 \pi \varepsilon_0 r^2} \quad r \geq \mathrm{R} \\\\ \&amp; &amp; \\\\ \mathrm{E}=\frac{\mathrm{Q} r}{4 \pi \varepsilon_0 \mathrm{R}^3} \quad r \leq \mathrm{R} \end{array} $$<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}$$ &lt; $${\\Phi _2}$$ = $${\\Phi _3}$$ &gt; $${\\Phi _4}$$"}, {"identifier": "B", "content": "$${\\Phi _1}$$ &gt; $${\\Phi _2}$$ &gt; $${\\Phi _3}$$ &gt; $${\\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>$$\rho(r)= \begin{cases}\rho_{0}\left(\frac{3}{4}-\frac{r}{R}\right) &amp; \text { for } r \leq R \\ \text { zero } &amp; \text { for } r&gt;R\end{cases}$$</p> <p>Where, $$r(r &lt; R)$$ 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