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YkefiN3lSqNIJjbG | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | The magnetic field due to a current carrying circular loop of radius $$3$$ $$cm$$ at a point on the axis at a distance of $$4$$ $$cm$$ from the centre is $$54\,\mu T.$$ What will be its value at the center of loop? | [{"identifier": "A", "content": "$$125\\,\\mu T$$ "}, {"identifier": "B", "content": "$$150\\,\\mu T$$ "}, {"identifier": "C", "content": "$$250\\,\\mu T$$ "}, {"identifier": "D", "content": "$$75\\,\\mu T$$ "}] | ["C"] | null | The magnetic field at a point on the axis of a circular loop at a distance $$x$$ from center is,
<br><br>$$B = {{{\mu _0}i\,{a^2}} \over {2\left( {{x^2} + {a^2}} \right)3/2}}$$ $$\,\,\,\,\,B' = {{{\mu _0}i} \over {2a}}$$
<br><br>$$\therefore$$ $$B' = {{B.{{\left( {{x^2} + {a^2}} \right)}^{3/2}}} \over {{a^3}}}$$
<br><... | mcq | aieee-2004 | 11,809 |
aMzGAKu0xbErsKMz | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is $$B.$$ It is then bent into a circular loop of $$n$$ turns. The magnetic field at the center of the coil will be | [{"identifier": "A", "content": "$$2n$$ $$B$$"}, {"identifier": "B", "content": "$${n^2}\\,B$$ "}, {"identifier": "C", "content": "$$nB$$ "}, {"identifier": "D", "content": "$$2{n^2}\\,B$$ "}] | ["B"] | null | <b>KEY CONCEPT : </b> Magnetic field at the center of a circular coil of radius $$R$$ carrying
<br><br>current is $$B = {{{\mu _0}i} \over {2R}}$$
<br><br>Given: $$n \times \left( {2\pi r'} \right) = 2\pi R$$
<br><br>$$ \Rightarrow nr' = R\,\,\,\,\,\,\,\,\,\,\,...\left( 1 \right)$$
<br><br>$$B' = {{n.{\mu _0}i} \over... | mcq | aieee-2004 | 11,810 |
DEJ0ZORcycCycSqo | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | Two concentric coils each of radius equal to $$2$$ $$\pi $$ $$cm$$ are placed at right angles to each other. $$3$$ ampere and $$4$$ ampere are the currents flowing in each coil respectively . The magnetic induction in Weber / $${m^2}$$ at the center of the coils will be
<br/>$$\left( {\mu = 4\pi \times {{10}^{ - 7... | [{"identifier": "A", "content": "$${10^{ - 5}}$$ "}, {"identifier": "B", "content": "$$12 \\times {10^{ - 5}}$$ "}, {"identifier": "C", "content": "$$7 \\times {10^{ - 5}}$$"}, {"identifier": "D", "content": "$$5 \\times {10^{ - 5}}$$"}] | ["D"] | null | <img class="question-image" src="https://imagex.cdn.examgoal.net/NNh4iJQMtysxDhHXw/cjZQNDlhqN9oRztD4zGDhBXtkMDvn/IYMJgpahUFPaQHSdo6PlDz/image.svg" loading="lazy" alt="AIEEE 2005 Physics - Magnetic Effect of Current Question 188 English Explanation">
<br><br>The magnetic field due to circular coil $$1$$ and $$2$$ are
<b... | mcq | aieee-2005 | 11,811 |
kTfJS2Muy0aneH3p | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | A long solenoid has $$200$$ turns per $$cm$$ and carries a current $$i.$$ The magnetic field at its center is $$6.28 \times {10^{ - 2}}\,\,\,Weber/{m^2}.$$ Another long solenoid has $$100$$ turns per $$cm$$ and it carries a current $${i \over 3}$$. The value of the magnetic field at its center is | [{"identifier": "A", "content": "$$1.05 \\times {10^{ - 2}}\\,\\,Weber/{m^2}$$ "}, {"identifier": "B", "content": "$$1.05 \\times {10^{ - 5}}\\,\\,Weber/{m^2}$$ "}, {"identifier": "C", "content": "$$1.05 \\times {10^{ - 3}}\\,\\,Weber/{m^2}$$ "}, {"identifier": "D", "content": "$$1.05 \\times {10^{ - 4}}\\,\\,Weber/{m^... | ["A"] | null | $${{{B_2}} \over {{B_1}}} = {{{\mu _0}{n_2}{i_2}} \over {{\mu _0}{n_1}{i_1}}}$$
<br><br>$$ \Rightarrow {{{B_2}} \over {6.28 \times {{10}^{ - 2}}}} = {{100 \times {i \over 3}} \over {200 \times i}}$$
<br><br>$$ \Rightarrow {B_2} = {{6.28 \times {{10}^{ - 2}}} \over 6}$$
<br><br>$$ = 1.05 \times {10^{ - 2}}\,\,Wb/{m^2}$$ | mcq | aieee-2006 | 11,812 |
1AGYz8zqqcvkX77q | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | Two identical conducting wires $$AOB$$ and $$COD$$ are placed at right angles to each other. The wire $$AOB$$ carries an electric current $${I_1}$$ and $$COD$$ carries a current $${I_2}$$. The magnetic field on a point lying at a distance $$d$$ from $$O$$, in a direction perpendicular to the plane of the wires $$AOB$$ ... | [{"identifier": "A", "content": "$${{{\\mu _0}} \\over {2\\pi d}}\\left( {I_1^2 + I_2^2} \\right)$$ "}, {"identifier": "B", "content": "$${{{\\mu _0}} \\over {2\\pi }}{\\left( {{{{I_1} + {I_2}} \\over d}} \\right)^{{1 \\over 2}}}$$ "}, {"identifier": "C", "content": "$${{{\\mu _0}} \\over {2\\pi d}}{\\left( {I_1^2 + I_... | ["C"] | null | Clearly, the magnetic fields at a point $$P,$$ equidistant from $$AOB$$ and $$COD$$ will have directions perpendicular to each other, as they are placed normal to each other.
<br><br>$$\therefore$$ Resultant field, $$B = \sqrt {B_1^2 + B_2^2} $$
<br><br>But $${B_1} = {{{\mu _0}{I_1}} \over {2\pi d}}$$ and $${B_2} = {... | mcq | aieee-2007 | 11,813 |
iNdr8BSAK0cZYxGI | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | A horizontal overhead powerline is at height of $$4m$$ from the ground and carries a current of $$100A$$ from east to west. The magnetic field directly below it on the ground is
<br/>$$\left( {{\mu _0} = 4\pi \times {{10}^{ - 7}}\,\,Tm\,\,{A^{ - 1}}} \right)$$ | [{"identifier": "A", "content": "$$2.5 \\times {10^{ - 7}}\\,T$$ southward "}, {"identifier": "B", "content": "$$5 \\times {10^{ - 6}}\\,T$$ northward "}, {"identifier": "C", "content": "$$5 \\times {10^{ - 6}}\\,T$$ southward "}, {"identifier": "D", "content": "$$2.5 \\times {10^{ - 7}}\\,T$$ northward "}] | ["C"] | null | The magnetic field is
<br><br>$$B = {{{\mu _0}} \over {4\pi }}{{2I} \over r}$$
<br><br>$$ = {10^{ - 7}} \times {{2 \times 100} \over 4}$$
<br><br>$$ = 5 \times {10^{ - 6}}T$$
<br><br><img class="question-image" src="https://imagex.cdn.examgoal.net/eAw9GIRclNRuJMCPv/FVkqNFdMW4Mqnh6uJEqThcxR1BWdI/HY0mT4vEaW7HD8ZbppADWE/... | mcq | aieee-2008 | 11,814 |
e34tGaWytOB3jjc1 | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | A current $$I$$ flows in an infinitely long wire with cross section in the form of a semi-circular ring of radius $$R.$$ The magnitude of the magnetic induction along its axis is: | [{"identifier": "A", "content": "$${{{\\mu _0}I} \\over {2{\\pi ^2}R}}$$ "}, {"identifier": "B", "content": "$${{{\\mu _0}I} \\over {2\\pi R}}$$ "}, {"identifier": "C", "content": "$${{{\\mu _0}I} \\over {4\\pi R}}$$ "}, {"identifier": "D", "content": "$${{{\\mu _0}I} \\over {{\\pi ^2}R}}$$ "}] | ["D"] | null | Current in a small element, $$dl = {{d\theta } \over \pi }I$$
<br><br>Magnetic field due to the element
<br><br>$$dB = {{{\mu _0}} \over {4\pi }}{{2dl} \over R}$$
<br><br>The component $$dB$$ $$\cos \,\theta ,$$ of the field is canceled by another opposite component.
<br><br>Therefore,
<br><br><img class="question-imag... | mcq | aieee-2011 | 11,816 |
r83EucwoXDFQfFmh | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | A charge $$Q$$ is uniformly distributed over the surface of non-conducting disc of radius $$R.$$ The disc rotates about an axis perpendicular to its plane and passing through its center with an angular velocity $$\omega .$$ As a result of this rotation a magnetic field of induction $$B$$ is obtained at the center of th... | [{"identifier": "A", "content": "<img class=\"question-image\" src=\"https://res.cloudinary.com/dckxllbjy/image/upload/v1734264850/exam_images/keghdjeesmndzirb6bke.webp\" loading=\"lazy\" alt=\"AIEEE 2012 Physics - Magnetic Effect of Current Question 170 English Option 1\"> "}, {"identifier": "B", "content": "<img clas... | ["A"] | null | The magnetic field due a disc is given as
<br><br>$$B = {{{h_0}\omega Q} \over {2\pi R}}$$ i.e., $$B \propto {1 \over R}$$ | mcq | aieee-2012 | 11,817 |
gyP9zjrGP7grn9me | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | Two identical wires $$A$$ and $$B,$$ each of length $$'l'$$, carry the same current $$I$$. Wire $$A$$ is bent into a circle of radius $$R$$ and wire $$B$$ is bent to form a square of side $$'a'$$. If $${B_A}$$ and $${B_B}$$ are the values of magnetic fields at the centres of the circle and square respectively, then the... | [{"identifier": "A", "content": "$${{{\\pi ^2}} \\over {16}}$$ "}, {"identifier": "B", "content": "$${{{\\pi ^2}} \\over {8\\sqrt 2 }}$$"}, {"identifier": "C", "content": "$${{{\\pi ^2}} \\over {8}}$$"}, {"identifier": "D", "content": "$${{{\\pi ^2}} \\over {16\\sqrt 2 }}$$ "}] | ["B"] | null | <b>Case (a) :</b>
<br><br><img class="question-image" src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734267739/exam_images/omhiwaxuh85ifnb0rtye.webp" loading="lazy" alt="JEE Main 2016 (Offline) Physics - Magnetic Effect of Current Question 175 English Explanation 1">
<br><br>$${B_A} = {{{\mu _0}} \over {4\pi... | mcq | jee-main-2016-offline | 11,818 |
liSnQLs1rbNsiHJs | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the
loop is B<sub>1</sub>. When the dipole moment is doubled by keeping the current constant, the magnetic field at the
centre of the loop is $${{B_2}}$$. The ratio $${{{B_1}} \over {{B_2}}}$$ is: | [{"identifier": "A", "content": "2"}, {"identifier": "B", "content": "$$\\sqrt 3 $$"}, {"identifier": "C", "content": "$$\\sqrt 2 $$"}, {"identifier": "D", "content": "$$1 \\over \\sqrt 2 $$"}] | ["C"] | null | Dipole moment, M = IA
<br><br>Let radius of circular loop = R
<br><br>$$\therefore\,\,\,$$ M = I $$ \times $$ $$\pi $$R<sup>2</sup>
<br><br>Later, we keep current constant ,
<br><br>But dipole moment becomes double, let new radius = R<sub>1</sub>
<br><br>$$\therefore\,\,\,$$ 2M = I $$ \times $... | mcq | jee-main-2018-offline | 11,819 |
tW4AspHuiLFEFKSKBMl8v | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | A Helmholtz coil has a pair of loops, each with $$N$$ turns and radius $$R$$. They are placed coaxially at distance $$R$$ and the same current $${\rm I}$$ flows through the loops in the same direction. $$P,$$ midway between the centers $$A$$ and $$C$$, is given by [Refer to figure given below] :
<br/><br/><img src="dat... | [{"identifier": "A", "content": "$${{8N{\\mu _0}{\\rm I}} \\over {{5^{1/2}}R}}$$ "}, {"identifier": "B", "content": "$${{8N{\\mu _0}{\\rm I}} \\over {{5^{3/2}}R}}$$ "}, {"identifier": "C", "content": "$${{4N{\\mu _0}{\\rm I}} \\over {{5^{1/2}}R}}$$"}, {"identifier": "D", "content": "$${{4N{\\mu _0}{\\rm I}} \\over {{5^... | ["B"] | null | P is the mid-point of line AC. A and C are the center of the two circle of each radius R.
<br><br>Current flows through loop A and B are in same direction, So the magnetic field will also be in the same direction. Magnitude of magnetic field at paint P
<br><br>= magnitude of magnetic field due to A and B at pain... | mcq | jee-main-2018-online-15th-april-morning-slot | 11,820 |
iOVtqRFyzIOL0auuW4PAO | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | A current of 1 A is flowing on the sides of an equilateral triangle of side 4.5 $$ \times $$ 10<sup>-2</sup> m. The magnetic field at the center of the triangle will be : | [{"identifier": "A", "content": "2 $$ \\times $$ 10<sup>-5</sup> Wb/m<sup>2</sup> "}, {"identifier": "B", "content": "Zero"}, {"identifier": "C", "content": "8 $$ \\times $$ 10<sup>-5</sup> Wb/m<sup>2</sup>"}, {"identifier": "D", "content": "4 $$ \\times $$ 10<sup>-5</sup> Wb/m<sup>2</sup>"}] | ["D"] | null | <p>We know that magnetic field due to finite current carrying wire is</p>
<p>$$B = {{{\mu _0}} \over {4\pi }}{I \over b}(\cos {\theta _1} + \cos {\theta _2})$$ ..... (1)</p>
<p> <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l3311zxe/77ff114d-3edb-4ed5-8034-95f7d4a38fcb/bebc0020-d1f4-11ec-b83f-ebfea68... | mcq | jee-main-2018-online-15th-april-evening-slot | 11,821 |
0GXgqSiobvpcWL9JF4Px4 | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | As shown in the figure, two infinitely long, identical wires are bent by 90<sup>o</sup> and placed in such a way that the segments LP and QM are along the x-axis, while segments PS and QN are parallel to the y-axis. If OP = OQ = 4cm, and the magnitude of the magnetic field at O is 10<sup>–4</sup> T, and the two wires c... | [{"identifier": "A", "content": "40 A, perpendicular into the page "}, {"identifier": "B", "content": "40 A, perpendicular out of the page"}, {"identifier": "C", "content": "20 A, perpendicular into the page"}, {"identifier": "D", "content": "40 A, perpendicular out of the page\n"}] | ["C"] | null | Magnetic field at 'O' will be done to 'PS' and 'QN' Only
<br><br>i.e. B<sub>0</sub> = B<sub>PS</sub> + B<sub>QN</sub> $$ \to $$ Both inwards
<br><br>Let current in each wire = i
<br><br>$$ \therefore $$ B<sub>0</sub> = $${{{\mu _0}i} \over {4\pi d}} + {{{\mu _0}i} \over {4\pi d}}$$
<br><br>or &nbs... | mcq | jee-main-2019-online-12th-january-morning-slot | 11,822 |
i7RjAPQQbWR7YrMMlf3rsa0w2w9jx3dntoy | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | A thin ring of 10 cm radius carries a uniformly distributed charge. The ring rotates at a constant angular
speed of 40 $$\pi $$ rad s<sup>–1</sup>
about its axis, perpendicular to its plane. If the magnetic field at its centre is 3.8 × 10<sup>–9</sup>
T, then the charge carried by the ring is close to ($$\mu $$<sub>0<... | [{"identifier": "A", "content": "7 \u00d7 10<sup>\u20136</sup> C"}, {"identifier": "B", "content": "4 \u00d7 10<sup>\u20135</sup> C"}, {"identifier": "C", "content": "2 \u00d7 10<sup>\u20136</sup> C"}, {"identifier": "D", "content": "3 \u00d7 10<sup>\u20135</sup> C"}] | ["D"] | null | $$B = {{{\mu _0}i} \over {2a}}{{\omega q} \over {2\pi }} = i$$<br><br>
$$B = {{{\mu _0}} \over {2a}}.{{\omega q} \over {2\pi }}$$<br><br>
$$B = {{{{10}^{ - 7}} \times 40} \over {0.1}} \times q \times \pi $$<br><br>
$$ \Rightarrow q = 3 \times {10^{ - 5}}C$$ | mcq | jee-main-2019-online-12th-april-morning-slot | 11,824 |
TJteEvhVtRYzb5bZbW3rsa0w2w9jwzjyd8u | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | The magnitude of the magnetic field at the centre of an equilateral triangular loop of side 1 m which is
carrying a current of 10 A is : <br/>[Take $$\mu $$<sub>0</sub> = 4$$\pi $$ × 10<sup>–7</sup>
NA<sup>–2</sup>] | [{"identifier": "A", "content": "3 $$\\mu $$T"}, {"identifier": "B", "content": "18 $$\\mu $$T"}, {"identifier": "C", "content": "9 $$\\mu $$T"}, {"identifier": "D", "content": "1 $$\\mu $$T"}] | ["B"] | null | For a current carrying wire, magnetic field at
a distance r is given by
<br><br><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1lfv1ok23/56d4c07e-ff3a-48fb-b4c4-439eadace6e9/bcd0f5b0-ceef-11ed-b0f4-95adde9456d2/file-1lfv1ok24.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1lfv1o... | mcq | jee-main-2019-online-10th-april-evening-slot | 11,825 |
ue0ZrEiwYks1ZfPOGqhdW | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | One of the two identical conducting wires of length L is bent in the form of a circular loop and the other one into a circular coil of N identical turns. If the same current is passed in both, the radio of the magnetic field at the central of the loop (B<sub>L</sub>) to that at the center of the coil (B<sub>C</sub>), ... | [{"identifier": "A", "content": "N"}, {"identifier": "B", "content": "$${1 \\over N}$$"}, {"identifier": "C", "content": "N<sup>2</sup>"}, {"identifier": "D", "content": "$${1 \\over {{N^2}}}$$"}] | ["D"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734263543/exam_images/ou2pubwdyl6gy3vopor1.webp" style="max-width: 100%; height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2019 (Online) 9th January Evening Slot Physics - Magnetic Effect of Current Question 153 English Explanation">... | mcq | jee-main-2019-online-9th-january-evening-slot | 11,827 |
VcReOlDT8osNmmOyLc7k9k2k5hhaa55 | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | A very long wire ABDMNDC is shown in
figure carrying current I. AB and BC parts are
straight, long and at right angle. At D wire
forms a circular turn DMND of radius R. AB,
BC parts are tangential to circular turn at N and
D. Magnetic field at the centre of circle is :
<img src="data:image/png;base64,UklGRm4GAABXRUJQVl... | [{"identifier": "A", "content": "$${{{\\mu _0}I} \\over {2\\pi R}}\\left( {\\pi + 1} \\right)$$"}, {"identifier": "B", "content": "$${{{\\mu _0}I} \\over {2\\pi R}}\\left( {\\pi - {1 \\over {\\sqrt 2 }}} \\right)$$"}, {"identifier": "C", "content": "$${{{\\mu _0}I} \\over {2R}}$$"}, {"identifier": "D", "content": "$$... | ["D"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734267484/exam_images/qs3bmn13wwcr5yodzjtl.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 8th January Evening Slot Physics - Magnetic Effect of Current Question 130 English Explanation">
<... | mcq | jee-main-2020-online-8th-january-evening-slot | 11,829 |
1ym8Ufjf4ERdX6s42Ajgy2xuketzv183 | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | A wire A, bent in the shape of an arc of a circle, carrying a current of 2 A and having radius 2 cm and another wire B, also bent in the shape of arc of a circle, carrying a current of 3 A and having radius of 4 cm, are placed as shown in the figure. The ratio of the magnetic fields due to the wires A and B at the comm... | [{"identifier": "A", "content": "4 : 6"}, {"identifier": "B", "content": "6 : 4"}, {"identifier": "C", "content": "2 : 5"}, {"identifier": "D", "content": "6 : 5"}] | ["D"] | null | Using formula, $$B = {{{\mu _0}i} \over {2r}}\left( {{\theta \over {2\pi }}} \right)$$
<br><br>$${B_A} = {{\mu (2)\left( {{{3\pi } \over 2}} \right)} \over {2(a)(2\pi )}} = {{3\mu } \over {4a}}$$<br><br>$${B_B} = {{\mu (3)\left( {{{5\pi } \over 3}} \right)} \over {2(2a)(2\pi )}} = {{5\mu } \over {8a}}$$<br><br>$$ \the... | mcq | jee-main-2020-online-4th-september-morning-slot | 11,830 |
yQxQFbjWuaPDxeGEri1klrx359q | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | Magnetic fields at two points on the axis of a circular coil at a distance of 0.05 m and 0.2 m from the centre are in the ratio 8 : 1. The radius of coil is ________. | [{"identifier": "A", "content": "1.0 m"}, {"identifier": "B", "content": "0.15 m"}, {"identifier": "C", "content": "0.2 m"}, {"identifier": "D", "content": "0.1 m"}] | ["D"] | null | <picture><source media="(max-width: 320px)" srcset="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266765/exam_images/nljm41ajjsohxbgknheq.webp"><source media="(max-width: 500px)" srcset="https://res.cloudinary.com/dckxllbjy/image/upload/v1734263669/exam_images/uozjm6j5hbl0p3fhgajc.webp"><source media="(max-wid... | mcq | jee-main-2021-online-25th-february-morning-slot | 11,832 |
dmhKqMoSYyM95CbNG31kmj1zx26 | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | A solenoid of 1000 turns per metre has a core with relative permeability 500. Insulated windings of the solenoid carry an electric current of 5A. The magnetic flux density produced by the solenoid is : (permeability of free space = 4$$\pi$$ $$\times$$ 10<sup>$$-$$7</sup> H/m) | [{"identifier": "A", "content": "$$\\pi$$T"}, {"identifier": "B", "content": "2 $$\\times$$ 10<sup>$$-$$3</sup>$$\\pi$$ T"}, {"identifier": "C", "content": "10<sup>$$-$$4</sup>$$\\pi$$ T"}, {"identifier": "D", "content": "$${\\pi \\over 5}$$ T"}] | ["A"] | null | B = $$\mu$$ n i<br><br>B = $$\mu$$<sub>r</sub> $$\mu$$<sub>0</sub> n i<br><br>B = 500 $$\times$$ 4$$\pi$$ $$\times$$ 10<sup>$$-$$7</sup> $$\times$$ 10<sup>3</sup> $$\times$$ 5<br><br>B = $$\pi$$ $$\times$$ 10<sup>$$-$$3</sup> $$\times$$ 10<sup>3</sup><br><br>B = $$\pi$$ T | mcq | jee-main-2021-online-17th-march-morning-shift | 11,833 |
njNUpnV0KZlgCj0CJD1kmkaazbt | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | A hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the magnitude of a magnetic field at point P which lies on the centre of the semicircle?<br/><br/><img src="data:image/png;base64,UklGRmwEAABXRUJQVlA4IGAEAABQIQCdASrKAHMAPm00lkgkIqIhI3F7GIANiWlu3WBpKX+hn9J7cP7byqvsPlR/vv8v4... | [{"identifier": "A", "content": "$${{{\\mu _0}I} \\over {4\\pi r}}(2 - \\pi )$$"}, {"identifier": "B", "content": "$${{{\\mu _0}I} \\over {2\\pi r}}(2 - \\pi )$$"}, {"identifier": "C", "content": "$${{{\\mu _0}I} \\over {4\\pi r}}(2 + \\pi )$$"}, {"identifier": "D", "content": "$${{{\\mu _0}I} \\over {2\\pi r}}(2 + \\p... | ["C"] | null | $$B = {{{\mu _0}I} \over {4\pi r}} + {{{\mu _0}I} \over {4\pi r}} + {{{\mu _0}I} \over {4r}}$$<br><br>$$ = {{{\mu _0}I} \over {2\pi r}} + {{{\mu _0}I} \over {4r}}$$<br><br>$$ \Rightarrow $$ $$B = {{{\mu _0}I} \over {4\pi r}}(2 + \pi )$$ | mcq | jee-main-2021-online-17th-march-evening-shift | 11,834 |
1kta8799v | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | The fractional change in the magnetic field intensity at a distance 'r' from centre on the axis of current carrying coil of radius 'a' to the magnetic field intensity at the centre of the same coil is : (Take r < a) | [{"identifier": "A", "content": "$${3 \\over 2}{{{a^2}} \\over {{r^2}}}$$"}, {"identifier": "B", "content": "$${2 \\over 3}{{{a^2}} \\over {{r^2}}}$$"}, {"identifier": "C", "content": "$${2 \\over 3}{{{r^2}} \\over {{a^2}}}$$"}, {"identifier": "D", "content": "$${3 \\over 2}{{{r^2}} \\over {{a^2}}}$$"}] | ["D"] | null | $${B_{axis}} = {{{\mu _0}i{R^2}} \over {2{{({R^2} + {x^2})}^{3/2}}}}$$<br><br>$${B_{centre}} = {{{\mu _0}i} \over {2R}}$$<br><br>$$\therefore$$ $${B_{centre}} = {{{\mu _0}i} \over {2a}}$$<br><br>$$\therefore$$ $${B_{axis}} = {{{\mu _0}i{a^2}} \over {2{{({a^2} + {r^2})}^{3/2}}}}$$<br><br>$$\therefore$$ fractional change... | mcq | jee-main-2021-online-26th-august-morning-shift | 11,837 |
1kth2q1zt | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | A coil having N turns is wound tightly in the form of a spiral with inner and outer radii 'a' and 'b' respectively. Find the magnetic field at centre, when a current I passes through coil: | [{"identifier": "A", "content": "$${{{\\mu _0}IN} \\over {2(b - a)}}{\\log _e}\\left( {{b \\over a}} \\right)$$"}, {"identifier": "B", "content": "$${{{\\mu _0}I} \\over 8}\\left[ {{{a + b} \\over {a - b}}} \\right]$$"}, {"identifier": "C", "content": "$${{{\\mu _0}I} \\over {4(a - b)}}\\left[ {{1 \\over a} - {1 \\over... | ["A"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734267483/exam_images/qt3c8zifwvldoiejd9xc.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 31st August Morning Shift Physics - Magnetic Effect of Current Question 94 English Explanation"><b... | mcq | jee-main-2021-online-31st-august-morning-shift | 11,839 |
1ktjmzsh5 | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | A current of 1.5 A is flowing through a triangle, of side 9 cm each. The magnetic field at the centroid of the triangle is :<br/><br/>(Assume that the current is flowing in the clockwise direction.) | [{"identifier": "A", "content": "3 $$\\times$$ 10<sup>$$-$$7</sup> T, outside the plane of triangle "}, {"identifier": "B", "content": "$$2\\sqrt 3 $$ $$\\times$$ 10<sup>$$-$$7</sup> T, outside the plane of triangle"}, {"identifier": "C", "content": "$$2\\sqrt 3 $$ $$\\times$$ 10<sup>$$-$$5</sup> T, inside the plane of... | ["D"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734264519/exam_images/k4hykytwfaapfiip6lbv.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 31st August Evening Shift Physics - Magnetic Effect of Current Question 93 English Explanation"> <... | mcq | jee-main-2021-online-31st-august-evening-shift | 11,840 |
1ktmqdiqv | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | There are two infinitely long straight current carrying conductors and they are held at right angles to each other so that their common ends meet at the origin as shown in the figure given below. The ratio of current in both conductor is 1 : 1. The magnetic field at point P is ____________.<br/><br/><img src="data:imag... | [{"identifier": "A", "content": "$${{{\\mu _0}I} \\over {4\\pi xy}}\\left[ {\\sqrt {{x^2} + {y^2}} + (x + y)} \\right]$$"}, {"identifier": "B", "content": "$${{{\\mu _0}I} \\over {4\\pi xy}}\\left[ {\\sqrt {{x^2} + {y^2}} - (x + y)} \\right]$$"}, {"identifier": "C", "content": "$${{{\\mu _0}Ixy} \\over {4\\pi }}\\lef... | ["A"] | null | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kwosh98t/244bc2b7-d997-4597-b554-4d5bfd9222a7/ef8a8bd0-5356-11ec-b443-85f16d0c41b6/file-1kwosh98u.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1kwosh98t/244bc2b7-d997-4597-b554-4d5bfd9222a7/ef8a8bd0-5356-11ec-b443-85f16d0c41b6/fi... | mcq | jee-main-2021-online-1st-september-evening-shift | 11,841 |
1l569abkd | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | <p>An infinitely long hollow conducting cylinder with radius R carries a uniform current along its surface.</p>
<p>Choose the correct representation of magnetic field (B) as a function of radial distance (r) from the axis of cylinder.</p> | [{"identifier": "A", "content": "<img src=\"https://app-content.cdn.examgoal.net/fly/@width/image/1l576bpz5/2c8a0081-fea7-47f9-a7b0-9c05cea815b2/ec23a400-fbd4-11ec-a656-a1c0c7b2ee13/file-1l576bpz6.png?format=png\" data-orsrc=\"https://app-content.cdn.examgoal.net/image/1l576bpz5/2c8a0081-fea7-47f9-a7b0-9c05cea815b2/ec2... | ["D"] | null | <p>Inside a hollow cylindrical conductor with uniform current distribution net magnetic field is zero in hollow space.</p>
<p>But outside the cylindrical conductor $$B \propto {1 \over r}$$</p>
<p>$$\Rightarrow$$ Graph in option D would be a correct one</p> | mcq | jee-main-2022-online-28th-june-morning-shift | 11,842 |
1l59p3xqc | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | <p>A long solenoid carrying a current produces a magnetic field B along its axis. If the current is doubled and the number of turns per cm is halved, the new value of magnetic field will be equal to</p> | [{"identifier": "A", "content": "B"}, {"identifier": "B", "content": "2B"}, {"identifier": "C", "content": "4B"}, {"identifier": "D", "content": "$${B \\over 2}$$"}] | ["A"] | null | <p>$$B = {\mu _0}ni$$</p>
<p>Now $$i \to 2i$$</p>
<p>And $$n \to {n \over 2}$$</p>
<p>$$B' = {\mu _0}{n \over 2} \times 2i = {\mu _0}ni = B$$</p> | mcq | jee-main-2022-online-25th-june-evening-shift | 11,843 |
1l5w2hdwb | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | <p>A coil of n number of turns wound tightly in the form of a spiral with inner and outer radii r<sub>1</sub> and r<sub>2</sub> respectively. When a current of strength I is passed through the coil, the magnetic field at its centre will be :</p> | [{"identifier": "A", "content": "$${{{\\mu _0}nI} \\over {2({r_2} - {r_1})}}$$"}, {"identifier": "B", "content": "$${{{\\mu _0}nI} \\over {{r_2}}}$$"}, {"identifier": "C", "content": "$${{{\\mu _0}nI} \\over {{r_2} - {r_1}}}{\\log _e}{{{r_1}} \\over {{r_2}}}$$"}, {"identifier": "D", "content": "$${{{\\mu _0}nI} \\over ... | ["D"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l6dmivyw/30c67313-ff9e-45d0-9dc4-0269dcf31df8/30c66d80-132d-11ed-a2ae-2bc5e0df659b/file-1l6dmivyx.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l6dmivyw/30c67313-ff9e-45d0-9dc4-0269dcf31df8/30c66d80-132d-11ed-a2ae-2bc5e0df659b... | mcq | jee-main-2022-online-30th-june-morning-shift | 11,845 |
1l6gmluyc | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | <p>$$\mathrm{B}_{X}$$ and $$\mathrm{B}_{\mathrm{Y}}$$ are the magnetic fields at the centre of two coils $$\mathrm{X}$$ and $$\mathrm{Y}$$ respectively each carrying equal current. If coil $$X$$ has 200 turns and $$20 \mathrm{~cm}$$ radius and coil $$Y$$ has 400 turns and $$20 \mathrm{~cm}$$ radius, the ratio of $$B_{X... | [{"identifier": "A", "content": "1 : 1"}, {"identifier": "B", "content": "1 : 2"}, {"identifier": "C", "content": "2 : 1"}, {"identifier": "D", "content": "4 : 1"}] | ["B"] | null | <p>$$B = {{{\mu _0}NI} \over {2R}}$$</p>
<p>$${{{B_X}} \over {{B_Y}}} = {{{N_x}{R_y}} \over {{N_y}{R_x}}}$$</p>
<p>$$ = {{200 \times 20} \over {400 \times 20}} = {1 \over 2}$$</p> | mcq | jee-main-2022-online-26th-july-morning-shift | 11,846 |
1ldnxffrw | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | <p>As shown in the figure, a long straight conductor with semicircular arc of radius $$\frac{\pi}{10}$$m is carrying current $$\mathrm{I=3A}$$. The magnitude of the magnetic field, at the center O of the arc is :</p>
<p>(The permeability of the vacuum $$=4\pi\times10^{-7}~\mathrm{NA}^{-2}$$)</p>
<p><img src="data:image... | [{"identifier": "A", "content": "$$4\\mu\\mathrm{T}$$"}, {"identifier": "B", "content": "$$3\\mu\\mathrm{T}$$"}, {"identifier": "C", "content": "$$6\\mu\\mathrm{T}$$"}, {"identifier": "D", "content": "$$1\\mu\\mathrm{T}$$"}] | ["B"] | null | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1ldodban9/90760155-e6e9-488e-8dc2-07b3df0bf6bf/4e45dd50-a3ab-11ed-bed3-417993225459/file-1ldodbana.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1ldodban9/90760155-e6e9-488e-8dc2-07b3df0bf6bf/4e45dd50-a3ab-11ed-bed3-417993225459/fi... | mcq | jee-main-2023-online-1st-february-evening-shift | 11,849 |
ldo6x4hj | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | A long conducting wire having a current I flowing through it, is bent into a circular coil of $\mathrm{N}$ turns. Then it is bent into a circular coil of $\mathrm{n}$ turns. The magnetic field is calculated at the centre of coils in both the cases. The ratio of the magnetic field in first case to that of second case is... | [{"identifier": "A", "content": "$ N^{2}: n^{2}$"}, {"identifier": "B", "content": "$\\mathrm{N}: \\mathrm{n}$"}, {"identifier": "C", "content": "$\\mathrm{n}: \\mathrm{N}$"}, {"identifier": "D", "content": "$n^{2}: N^{2}$"}] | ["A"] | null | $I=(2 \pi r) n$
<br/><br/>$$
\begin{aligned}
& r \propto\left(\frac{I}{n}\right) \\\\
& B=n\left(\frac{\mu_{0} i}{2 r}\right) \propto\left(\frac{\mu_{0} i}{2 L}\right) n^{2} \\\\
& \frac{B_{1}}{B_{2}}=\left(\frac{N^{2}}{n^{2}}\right)
\end{aligned}
$$ | mcq | jee-main-2023-online-31st-january-evening-shift | 11,850 |
1ldof7otr | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | <p>Find the magnetic field at the point $$\mathrm{P}$$ in figure. The curved portion is a semicircle connected to two long straight wires.</p>
<p><img src="data:image/png;base64,UklGRu4IAABXRUJQVlA4IOIIAACQrQCdASoUAgADP4HA3mW2MS6nIZSIssAwCWlu4XHF7mNwvj6q9Kd7VhT2sk8fcTMziMNH31+jJmWscKPSt8eV6GkjhR6VvjyvQ0kcKPSt8eUweCZ0s0... | [{"identifier": "A", "content": "$$\\frac{\\mu_{0} i}{2 r}\\left(\\frac{1}{2}+\\frac{1}{2 \\pi}\\right)$$"}, {"identifier": "B", "content": "$$\\frac{\\mu_{\\mathrm{o}} i}{2 r}\\left(1+\\frac{2}{\\pi}\\right)$$"}, {"identifier": "C", "content": "$$\\frac{\\mu_{0} \\dot{i}}{2 r}\\left(\\frac{1}{2}+\\frac{1}{\\pi}\\right... | ["A"] | null | $$
B_{\mathrm{P}}=\left(\frac{\mu_0 i}{4 r}+\frac{\mu_0 i}{4 \pi r}\right)=\frac{\mu_0 i}{2 r}\left(\frac{1}{2}+\frac{1}{2 \pi}\right)
$$ | mcq | jee-main-2023-online-1st-february-morning-shift | 11,851 |
ldqvqyva | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | <p>As shown in the figure, a current of $2 \mathrm{~A}$ flowing in an equilateral triangle of side $4 \sqrt{3} \mathrm{~cm}$. The magnetic field at the centroid $\mathrm{O}$ of the triangle is</p>
<p><img src="data:image/png;base64,UklGRhQOAABXRUJQVlA4IAgOAADQ+wCdASoAA6oCP4HA2WY2MKynIXHI+sAwCWlu/CX4S2HnZ1+ftz/sPW5dDcmu... | [{"identifier": "A", "content": "$4 \\sqrt{3} \\times 10^{-4} \\mathrm{~T}$"}, {"identifier": "B", "content": "$4 \\sqrt{3} \\times 10^{-5} \\mathrm{~T}$"}, {"identifier": "C", "content": "$3 \\sqrt{3} \\times 10^{-5} \\mathrm{~T} $"}, {"identifier": "D", "content": "$\\sqrt{3} \\times 10^{-4} \\mathrm{~T}$"}] | ["C"] | null | <p>$${B_{net}} = {{{\mu _0}i} \over {4\pi r}}(\sin \alpha + \sin \beta ) \times 3$$</p>
<p>$$ = {{{\mu _0} \times 2} \over {4\pi \times (2 \times {{10}^{ - 2}})}} \times \left( {{{\sqrt 3 } \over 2} + {{\sqrt 3 } \over 2}} \right) \times 3$$</p>
<p>$$ = {10^{ - 7}} \times {10^2}(3\sqrt 3 )$$</p>
<p>$$ = 3\sqrt 3 \ti... | mcq | jee-main-2023-online-30th-january-evening-shift | 11,852 |
1ldsanxdr | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | <p>The electric current in a circular coil of four turns produces a magnetic induction 32 T at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by the same current will be :</p> | [{"identifier": "A", "content": "2 T"}, {"identifier": "B", "content": "4 T"}, {"identifier": "C", "content": "8 T"}, {"identifier": "D", "content": "16 T"}] | ["A"] | null | <p>By given information</p>
<p>$$32 = 4 \times {{{\mu _0}i} \over {2r}}$$ ..... (i)</p>
<p>Also, $$r' = 4r$$ ...... (ii)</p>
<p>and $$B' = 1 \times {{{\mu _0}i} \over {2r'}}$$ .... (iii)</p>
<p>$$ \Rightarrow B' = {{{\mu _0}i} \over {2(4r)}} = {{{\mu _0}i} \over {8r}} = {1 \over 8} \times 16 = 2\,T$$</p> | mcq | jee-main-2023-online-29th-january-evening-shift | 11,853 |
1ldsogf9h | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | <p>The magnitude of magnetic induction at mid point $$\mathrm{O}$$ due to current arrangement as shown in Fig will be</p>
<p><img src="data:image/png;base64,UklGRiIIAABXRUJQVlA4IBYIAABQkwCdASoAAwQCP4HA3Ga2MK2noLJ4ssAwCWlu/E85bU2nZ1+fr7jG2H9nd2w77jdTB0tv0Jbrpy4vM9ARl105cXksdUMSwNrcz0BGXXTlxeZ6AjLrpy4vM9ANzGJXTlxeZ6AjLrp... | [{"identifier": "A", "content": "$$\\frac{\\mu_{0} I}{\\pi a}$$"}, {"identifier": "B", "content": "$$\\frac{\\mu_{0} I}{4 \\pi a}$$"}, {"identifier": "C", "content": "$$\\frac{\\mu_{0} I}{2 \\pi a}$$"}, {"identifier": "D", "content": "0"}] | ["A"] | null | Magnetic field due to wire $A B$ and wire $E D$ cancel each other. So, magnetic field due to BC and ET will be
<br/><br/>$$
\begin{aligned}
& B_1=\frac{\mu_0 I}{4 \pi(a / 2)} \cdot\left(\sin \frac{\pi}{2}+\sin 0^{\circ}\right) = \frac{\mu_0 I}{2 \pi a} \\
& B_2=\frac{\mu_0 I}{4 \pi(a / 2)} \cdot\left(\sin \frac{\pi}{2}... | mcq | jee-main-2023-online-29th-january-morning-shift | 11,854 |
1ldspgpze | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | <p>A single current carrying loop of wire carrying current I flowing in anticlockwise direction seen from +ve $$\mathrm{z}$$ direction and lying in $$x y$$ plane is shown in figure. The plot of $$\hat{j}$$ component of magnetic field (By) at a distance '$$a$$' (less than radius of the coil) and on $$y z$$ plane vs $$z$... | [{"identifier": "A", "content": "<img src=\"https://app-content.cdn.examgoal.net/fly/@width/image/1ldt1b27h/5fd8527f-12ab-49da-a31f-5907c344d890/4573a9d0-a63c-11ed-8e98-03be028140e9/file-1ldt1b27i.png?format=png\" data-orsrc=\"https://app-content.cdn.examgoal.net/image/1ldt1b27h/5fd8527f-12ab-49da-a31f-5907c344d890/457... | ["D"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1lei2jbse/0b155214-c8a1-4778-a4ba-55cd9822edc8/acb0a1d0-b400-11ed-bf7e-c52177c53cde/file-1lei2jbsf.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1lei2jbse/0b155214-c8a1-4778-a4ba-55cd9822edc8/acb0a1d0-b400-11ed-bf7e-c52177c53cde... | mcq | jee-main-2023-online-29th-january-morning-shift | 11,855 |
1lduh5pkk | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | <p>Match List I with List II</p>
<p><style type="text/css">
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidden;padding:10px 5px;word-break:normal;}
.tg th{border-color:black;border-style:solid;bo... | [{"identifier": "A", "content": "A-III, B-IV, C-I, D-II"}, {"identifier": "B", "content": "A-II, B-I, C-IV, D-III"}, {"identifier": "C", "content": "A-III, B-I, C-IV, D-II"}, {"identifier": "D", "content": "A-I, B-III, C-IV, D-II"}] | ["C"] | null | $A \rightarrow B_{0}=\frac{-\mu_{0} I}{4 \pi r}+\frac{\mu_{0} I}{2 r}-\frac{\mu_{0} I}{4 \pi r}$
<br/><br/>
$$
B_{0}=\frac{\mu_{0} I}{2 \pi r}(\pi-1) \quad A \rightarrow \text { III }
$$<br/><br/>
$B \rightarrow B_{0}=\frac{\mu_{0} I}{4 \pi r}+\frac{\mu_{0} I}{4 r}+\frac{\mu_{0} I}{4 \pi r}$
<br/><br/>
$$
B_{0}=\frac{... | mcq | jee-main-2023-online-25th-january-morning-shift | 11,857 |
1ldwqnmpd | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | <p>A long solenoid is formed by winding 70 turns cm$$^{-1}$$. If 2.0 A current flows, then the magnetic field produced inside the solenoid is ____________ ($$\mu_0=4\pi\times10^{-7}$$ TmA$$^{-1}$$)</p> | [{"identifier": "A", "content": "$$88\\times10^{-4}$$ T"}, {"identifier": "B", "content": "$$1232\\times10^{-4}$$ T"}, {"identifier": "C", "content": "$$176\\times10^{-4}$$ T"}, {"identifier": "D", "content": "$$352\\times10^{-4}$$ T"}] | ["C"] | null | Number of turns per meter $=7000$ turns per $\mathrm{m}$
<br/><br/>
$$
\begin{aligned}
&i=2 \mathrm{~A} & \\\\
& B=\mu_{0} n i =4 \pi \times 10^{-7} \times 7000 \times 2 \\\\
& =56 \pi \times 10^{-4} \mathrm{~T} \\\\
& =56 \times \frac{22}{7} \times 10^{-4} \mathrm{~T} \\\\
& =176 \times 10^{-4} \mathrm{~T}
\end{aligne... | mcq | jee-main-2023-online-24th-january-evening-shift | 11,858 |
1ldydj6mi | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | <p>A circular loop of radius $$r$$ is carrying current I A. The ratio of magnetic field at the center of circular loop and at a distance r from the center of the loop on its axis is :</p> | [{"identifier": "A", "content": "3$$\\sqrt2$$ : 2"}, {"identifier": "B", "content": "1 : 3$$\\sqrt2$$"}, {"identifier": "C", "content": "2$$\\sqrt2$$ : 1"}, {"identifier": "D", "content": "1 : $$\\sqrt2$$"}] | ["C"] | null | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1le1jbhf8/43f020d0-7d07-44c2-9c0d-b5a53dd02ca4/fab9ab40-aae8-11ed-b71e-0f88f2caf2c9/file-1le1jbhf9.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1le1jbhf8/43f020d0-7d07-44c2-9c0d-b5a53dd02ca4/fab9ab40-aae8-11ed-b71e-0f88f2caf2c9/fi... | mcq | jee-main-2023-online-24th-january-morning-shift | 11,859 |
1lgvsbrve | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | <p>A straight wire carrying a current of $$14 \mathrm{~A}$$ is bent into a semi-circular arc of radius $$2.2 \mathrm{~cm}$$ as shown in the figure. The magnetic field produced by the current at the centre $$(\mathrm{O})$$ of the arc. is ____________ $$\times ~10^{-4} \mathrm{~T}$$</p>
<p><img src="data:image/png;base64... | [] | null | 2 | $$
\begin{aligned}
& \mathrm{B}_{\text {at } \mathrm{O}}=\frac{\mu_0 \mathrm{I}}{4 \mathrm{R}}=\frac{4 \pi \times 10^{-7} \times 14}{4 \times 2.2 \times 10^{-2}} \\\\
& =2 \times 10^{-4} \mathrm{~T}
\end{aligned}
$$ | integer | jee-main-2023-online-10th-april-evening-shift | 11,860 |
1lh24yfpg | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | <p>A long straight wire of circular cross-section (radius a) is carrying steady current I. The current I is uniformly distributed across this cross-section. The magnetic field is</p> | [{"identifier": "A", "content": "uniform in the region $$r < a$$ and inversely proportional to distance $$r$$ from the axis, in the region $$r > a$$"}, {"identifier": "B", "content": "zero in the region $$r < a$$ and inversely proportional to $$r$$ in the region $$r > a$$"}, {"identifier": "C", "content": "directly pro... | ["C"] | null | <p>The magnetic field due to a current carrying wire can be calculated using Ampere's law. When the current is uniformly distributed across the cross-section of the wire, the situation will be different inside and outside the wire.</p>
<p>Inside the wire (r < a), the magnetic field is directly proportional to r ... | mcq | jee-main-2023-online-6th-april-morning-shift | 11,862 |
1lh25y0ny | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | <p>Two identical circular wires of radius $$20 \mathrm{~cm}$$ and carrying current $$\sqrt{2} \mathrm{~A}$$ are placed in perpendicular planes as shown in figure. The net magnetic field at the centre of the circular wires is __________ $$\times 10^{-8} \mathrm{~T}$$.</p>
<p><img src="data:image/png;base64,UklGRlQPAABXR... | [] | null | 628 | According to question,
<br><br><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1lh30jlo4/81246d74-28b1-4a6a-939f-f68ca6337e06/c675f340-e71d-11ed-ab3e-bf3b57063390/file-1lh30jlo5.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1lh30jlo4/81246d74-28b1-4a6a-939f-f68ca6337e06/c675f340... | integer | jee-main-2023-online-6th-april-morning-shift | 11,863 |
lsblkiz1 | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | A regular polygon of 6 sides is formed by bending a wire of length $4 \pi$ meter.<br/><br/> If an electric current of $4 \pi \sqrt{3}$ A is flowing through the sides of the polygon, the magnetic field at the centre of the polygon would be $x \times 10^{-7} \mathrm{~T}$. <br/><br/>The value of $x$ is _________. | [] | null | 72 | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lsqgqcor/e09d0d4d-f89f-4d75-9d0e-0bbbe0beefe6/7c5b68b0-cdc9-11ee-9975-55955dadf965/file-6y3zli1lsqgqcos.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/6y3zli1lsqgqcor/e09d0d4d-f89f-4d75-9d0e-0bbbe0beefe6/7c5b68b0-cdc9-11ee-99... | integer | jee-main-2024-online-1st-february-morning-shift | 11,864 |
jaoe38c1lsc4j6we | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | <p>Two long, straight wires carry equal currents in opposite directions as shown in figure. The separation between the wires is $$5.0 \mathrm{~cm}$$. The magnitude of the magnetic field at a point $$\mathrm{P}$$ midway between the wires is _______ $$\mu \mathrm{T}$$</p>
<p>(Given : $$\mu_0=4 \pi \times 10^{-7} \mathrm{... | [] | null | 160 | <p>$$\begin{aligned}
& \mathrm{B}=\left(\frac{\mu_0 \mathrm{i}}{2 \pi \mathrm{a}}\right) \times 2=\frac{4 \pi \times 10^{-7} \times 10}{\pi \times\left(\frac{5}{2} \times 10^{-2}\right)} \\
& =16 \times 10^{-5}=160 \mu \mathrm{T}
\end{aligned}$$</p> | integer | jee-main-2024-online-27th-january-morning-shift | 11,865 |
jaoe38c1lsd8hit8 | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | <p>Two circular coils $$P$$ and $$Q$$ of 100 turns each have same radius of $$\pi \mathrm{~cm}$$. The currents in $$P$$ and $$R$$ are $$1 A$$ and $$2 A$$ respectively. $$P$$ and $$Q$$ are placed with their planes mutually perpendicular with their centers coincide. The resultant magnetic field induction at the center of... | [] | null | 20 | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lsiirw03/b1ebf1e2-95ce-4fa4-b1c3-546c5c7b2a4f/34264130-c96b-11ee-b416-eff853096672/file-6y3zli1lsiirw04.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/6y3zli1lsiirw03/b1ebf1e2-95ce-4fa4-b1c3-546c5c7b2a4f/34264130-c96b-11ee... | integer | jee-main-2024-online-31st-january-evening-shift | 11,867 |
1lsg6z8kk | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | <p>The current of $$5 \mathrm{~A}$$ flows in a square loop of sides $$1 \mathrm{~m}$$ is placed in air. The magnetic field at the centre of the loop is $$X \sqrt{2} \times 10^{-7} T$$. The value of $$X$$ is _________.</p> | [] | null | 40 | <p>$$\begin{aligned}
& \mathrm{B}=4 \times \frac{\mu_0 \mathrm{i}}{4 \pi(1 / 2)}\left(\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}\right) \\
& =4 \times 10^{-7} \times 5 \times 2 \times \sqrt{2} \\
& -40 \sqrt{2} \times 10^{-7} \mathrm{~T}
\end{aligned}$$</p> | integer | jee-main-2024-online-30th-january-evening-shift | 11,868 |
1lsgdo9b3 | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | <p>Two insulated circular loop A and B of radius '$$a$$' carrying a current of '$$\mathrm{I}$$' in the anti clockwise direction as shown in the figure. The magnitude of the magnetic induction at the centre will be :</p>
<p><img src="data:image/png;base64,UklGRn4SAABXRUJQVlA4IHISAAAQEgGdASrDAgADP4HA2mY2L60nITCpIsAwCWlu/... | [{"identifier": "A", "content": "$$\\frac{\\sqrt{2} \\mu_0 I}{a}$$\n"}, {"identifier": "B", "content": "$$\\frac{\\mu_0 I}{\\sqrt{2} a}$$\n"}, {"identifier": "C", "content": "$$\\frac{\\mu_0 \\mathrm{I}}{2 \\mathrm{a}}$$\n"}, {"identifier": "D", "content": "$$\\frac{2 \\mu_0 I}{a}$$"}] | ["B"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lsqmdiia/1e006c76-2584-475d-bb0a-6c82b5ee4737/8e1bed20-cddf-11ee-a0d3-7b75c4537559/file-6y3zli1lsqmdiib.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/6y3zli1lsqmdiia/1e006c76-2584-475d-bb0a-6c82b5ee4737/8e1bed20-cddf-11ee... | mcq | jee-main-2024-online-30th-january-morning-shift | 11,869 |
lv2es35t | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | <p>Two parallel long current carrying wire separated by a distance $$2 r$$ are shown in the figure. The ratio of magnetic field at $$A$$ to the magnetic field produced at $$C$$ is $$\frac{x}{7}$$. The value of $$x$$ is __________.</p>
<p><img src="data:image/png;base64,UklGRpIGAABXRUJQVlA4IIYGAAAQZgCdASoAAygBP4HA22W2MK... | [] | null | 5 | <p>At point $$A$$</p>
<p>$$B_A=\frac{\mu_0 I}{2 \pi r}+\frac{\mu_0(2 I)}{2 \pi(3 r)}$$</p>
<p>At point $$C$$</p>
<p>$$\begin{aligned}
& B_C=\frac{\mu_0 I}{2 \pi(3 r)}+\frac{\mu_0(2 I)}{r} \\
& \Rightarrow \frac{B_A}{B_C}=\frac{5}{7}
\end{aligned}$$</p> | integer | jee-main-2024-online-4th-april-evening-shift | 11,870 |
lvc58ehc | physics | magnetics | biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire | <p>An element $$\Delta l=\Delta x\hat{i}$$ is placed at the origin and carries a large current $$I=10 \mathrm{~A}$$. The magnetic field on the $$y$$-axis at a distance of $$0.5 \mathrm{~m}$$ from the elements $$\Delta x$$ of $$1 \mathrm{~cm}$$ length is:</p>
<p><img src="data:image/png;base64,UklGRqgHAABXRUJQVlA4IJwHAA... | [{"identifier": "A", "content": "$$10 \\times 10^{-8} \\mathrm{~T}$$\n"}, {"identifier": "B", "content": "$$8 \\times 10^{-8} \\mathrm{~T}$$\n"}, {"identifier": "C", "content": "$$4 \\times 10^{-8} \\mathrm{~T}$$\n"}, {"identifier": "D", "content": "$$12 \\times 10^{-8} \\mathrm{~T}$$"}] | ["C"] | null | <p>$$\begin{aligned}
& B=\frac{u_0}{4 \pi} \frac{i d l \sin \theta}{r^2} \\
& \Rightarrow B=\frac{10^{-7} \times 10 \times 10 \quad \times 1}{\frac{1}{4}}=4 \times 10^{-8} \mathrm{~T}
\end{aligned}$$</p> | mcq | jee-main-2024-online-6th-april-morning-shift | 11,871 |
ToF8RimAwI5HL3ky | physics | magnetics | force-and-torque-on-current-carrying-conductor | Wires $$1$$ and $$2$$ carrying currents $$i{}_1$$ and $$i{}_2$$ respectively are inclined at an angle $$\theta $$ to each other. What is the force on a small element $$dl$$ of wire $$2$$ at a distance of $$r$$ from wire $$1$$ (as shown in figure) due to the magnetic field of wire $$1$$?
<img src="data:image/png;base64... | [{"identifier": "A", "content": "$${{{\\mu _0}} \\over {2\\pi r}}{i_1}{i_2}\\,dl\\,\\tan \\,\\theta $$ "}, {"identifier": "B", "content": "$${{{\\mu _0}} \\over {2\\pi r}}{i_1}{i_2}\\,dl\\,\\sin \\,\\theta $$ "}, {"identifier": "C", "content": "$${{{\\mu _0}} \\over {2\\pi r}}{i_1}{i_2}\\,dl\\,\\cos \\,\\theta $$ "}, {... | ["C"] | null | Magnetic field due to current in wire $$1$$ at point $$P$$ distant $$r$$ from the wire is
<br><br><img class="question-image" src="https://imagex.cdn.examgoal.net/TtHen0WXtOX5AwQhh/thmvyMSUPhFJrx9zSu0ka5WYUb9C2/RIkLInof4PDnnmUp1a5IE0/image.svg" loading="lazy" alt="AIEEE 2002 Physics - Magnetic Effect of Current Questio... | mcq | aieee-2002 | 11,872 |
DaFGDCYOPs7FhyoY | physics | magnetics | force-and-torque-on-current-carrying-conductor | Two long conductors, separated by a distance $$d$$ carry current $${I_1}$$ and $${I_2}$$ in the same direction. They exert a force $$F$$ on each other. Now the current in one of them is increased to two times and its direction is reversed. The distance is also increased to $$3d$$. The new value of the force between the... | [{"identifier": "A", "content": "$$ - {{2F} \\over 3}$$ "}, {"identifier": "B", "content": "$${F \\over 3}$$ "}, {"identifier": "C", "content": "$$-2F$$ "}, {"identifier": "D", "content": "$$ - {F \\over 3}$$ "}] | ["A"] | null | Force between two long conductor carrying current,
<br><br>$$F = {{{\mu _0}} \over {4\pi }}{{2{I_1}{I_2}} \over d} \times \ell $$
<br><br>$$F' = - {{{\mu _0}} \over {4\pi }}{{2\left( {2{I_1}} \right){I_2}} \over {3d}}\ell $$
<br><br>$$\therefore$$ $${{F'} \over F} = {{ - 2} \over 3}$$ | mcq | aieee-2004 | 11,873 |
nvrFinNnXyrHel6C | physics | magnetics | force-and-torque-on-current-carrying-conductor | Two thin, long, parallel wires, separated by a distance $$'d'$$ carry a current of $$'i'$$ $$A$$ in the same direction. They will | [{"identifier": "A", "content": "repel each other with a force of $${\\mu _0}{i^2}/\\left( {2\\pi d} \\right)$$ "}, {"identifier": "B", "content": "attract each other with a force of $${\\mu _0}{i^2}/\\left( {2\\pi d} \\right)$$ "}, {"identifier": "C", "content": "repel each other with a force $$_0{i^2}/\\left( {2\\pi ... | ["B"] | null | $${F \over \ell } = {{{\mu _0}{i_1}} \over {2\pi d}} = {{{\mu _0}{i^2}} \over {2\pi d}}$$
<br><br><img class="question-image" src="https://imagex.cdn.examgoal.net/81YmX4ZokJp4ZKSZ4/X1bRoMz04nlbDYg0ZppqZDQ0EU1Pb/sKBngKbEbfA5HYjEXHVEZF/image.svg" loading="lazy" alt="AIEEE 2005 Physics - Magnetic Effect of Current Questio... | mcq | aieee-2005 | 11,874 |
HT6CyvbQWbymnkIw | physics | magnetics | force-and-torque-on-current-carrying-conductor | Two long parallel wires are at a distance $$2d$$ apart. They carry steady equal currents flowing out of the plane of the paper as shown. The variation of the magnetic field $$B$$ along the line $$XX'$$ is given by
| [{"identifier": "A", "content": "<img class=\"question-image\" src=\"https://imagex.cdn.examgoal.net/CfIrVI8LzaucHZMrs/AcuUmWZ2Vcog9r54rD4RWuwB4ZQL7/4ikFvUacmjCG0FfuQE6qW4/image.png\" loading=\"lazy\" alt=\"AIEEE 2010 Physics - Magnetic Effect of Current Question 171 English Option 1\"> "}, {"identifier": "B", "content... | ["A"] | null | The magnetic field varies inversely with the distance for a long conductor. That is, $$B \propto {1 \over d}.$$ According to the magnitude and direction shown graph $$(1)$$ is the correct one. | mcq | aieee-2010 | 11,876 |
o5riZKrbzx4V3Ck1 | physics | magnetics | force-and-torque-on-current-carrying-conductor | Two long current carrying thin wires, both with current $$I,$$ are held by insulating threads of length $$L$$ and are in equilibrium as shown in the figure, with threads making an angle $$'\theta '$$ with the vertical. If wires have mass $$\lambda $$ per unit-length then the value of $$I$$ is :
<br/>($$g=$$ $$gravitat... | [{"identifier": "A", "content": "$$2\\sqrt {{{\\pi gL} \\over {{\\mu _0}}}\\tan \\theta } $$ "}, {"identifier": "B", "content": "$$\\sqrt {{{\\pi \\lambda gL} \\over {{\\mu _0}}}\\tan \\theta } $$ "}, {"identifier": "C", "content": "$$\\sin \\theta \\sqrt {{{\\pi \\lambda gL} \\over {{\\mu _0}\\,\\cos \\theta }}} $$ "}... | ["D"] | null | Let us consider $$'\ell '$$ length of current carrying wire,
<br><br>At equilibrium
<br><br>$$T\cos \theta = \lambda g\ell $$
<br><br><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l91f8ury/49827386-97e5-4277-8921-73e46ec64f98/f833aee0-47db-11ed-8284-6d7e98c66709/file-1l91f8urz.png?format=png" data-o... | mcq | jee-main-2015-offline | 11,878 |
PgUpIGk8YOYt90whzkLyo | physics | magnetics | force-and-torque-on-current-carrying-conductor | A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle of 75<sup>o</sup>. One of the fields has a magnitude of 15 mT. The dipole attains stable equilibrium at an angle of 30<sup>o</sup> with this field. The magnitude of the other field (in mT ) is close to | [{"identifier": "A", "content": "11"}, {"identifier": "B", "content": "36"}, {"identifier": "C", "content": "1"}, {"identifier": "D", "content": "1060"}] | ["A"] | null | For equilibrium,
<br><br>net torque acting on dipole is = 0
<br><br>$$ \therefore $$ $$\tau $$<sub>1</sub> = $$\tau $$<sub>2</sub>
<br><br>$$ \Rightarrow $$ mB<sub>1</sub> sin$$\theta $$<sub>1</sub> = mB<sub>2</sub> sin$$\theta $$<sub>2</sub>
<br><br>$$ \Rightarrow $$  ... | mcq | jee-main-2016-online-9th-april-morning-slot | 11,879 |
Drlzzr2yckzbHOLvHl6fy | physics | magnetics | force-and-torque-on-current-carrying-conductor | A magnetic dipole in a constant magnetic field has :
| [{"identifier": "A", "content": "maximum potential energy when the torque is maximum.\n"}, {"identifier": "B", "content": "zero potential energy when the torque is minimum."}, {"identifier": "C", "content": "zero potential energy when the torque is maximum.\n"}, {"identifier": "D", "content": "minimum potential energy ... | ["C"] | null | In uniform magnetic field, the torque experienced by the magnetic dipole is $$\tau $$ = MB sin $$\theta $$
<br><br>Torque will be maximum when $$\theta $$ = 90<sup>o</sup>
<br><br>$$\tau $$<sub>max</sub> = MB sin90<sup>o</sup> = MB
<br><br>Potential energy of magnetic dipole,
<br><br>$$\mu $$ = $$-$$ MB cos $$\the... | mcq | jee-main-2017-online-8th-april-morning-slot | 11,880 |
oOaec27q1PPGSb1TLUOXI | physics | magnetics | force-and-torque-on-current-carrying-conductor | A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is : | [{"identifier": "A", "content": "away from the wire"}, {"identifier": "B", "content": "towards the wire"}, {"identifier": "C", "content": "parallel to the wire along the current"}, {"identifier": "D", "content": "parallel to the wire opposite to the current"}] | ["B"] | null | <p> <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kyl2xev0/ca028ecf-3aed-4c1d-9321-f76cbc6039c6/18471bc0-78e5-11ec-83c0-f7d0013bbaf7/file-1kyl2xev1.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1kyl2xev0/ca028ecf-3aed-4c1d-9321-f76cbc6039c6/18471bc0-78e5-11ec-83c0-f7d0013bbaf... | mcq | jee-main-2017-online-9th-april-morning-slot | 11,881 |
2qeCNfqnysklKZZjcjP7T | physics | magnetics | force-and-torque-on-current-carrying-conductor | A rectangular coil (Dimension 5 cm × 2.5 cm)
with 100 turns, carrying a current of 3 A in the
clock-wise direction is kept centered at the
origin and in the X-Z plane. A magnetic field
of 1 T is applied along X-axis. If the coil is tilted
through 45° about Z-axis, then the torque on
the coil is : | [{"identifier": "A", "content": "0.42 Nm"}, {"identifier": "B", "content": "0.55 Nm"}, {"identifier": "C", "content": "0.38 Nm"}, {"identifier": "D", "content": "0.27\nNm"}] | ["D"] | null | $$\left| {\overrightarrow \tau } \right| = \left| {\overline M \times \overline B } \right|$$<br><br>
$$\tau = NI \times A \times B \times \sin {45^o}$$<br><br>
$$\tau = 0.27 \,Nm$$ | mcq | jee-main-2019-online-9th-april-morning-slot | 11,882 |
kgLpohur2xA2AvAgaUgm0 | physics | magnetics | force-and-torque-on-current-carrying-conductor | A rigid square loop of side 'a' and carrying
current I<sub>2</sub> is lying on a horizontal surface near
a long current I<sub>1</sub> carrying wire in the same plane
as shown in figure. The net force on the loop
due to wire will be :
<img src="data:image/png;base64,UklGRrAFAABXRUJQVlA4IKQFAAAQVgCdASrsAhIBP4HA3mW2MS6nIN... | [{"identifier": "A", "content": "Repulsive and equal to $$\\mu $$<sub>0</sub>I<sub>1</sub>I<sub>2</sub>/4$$\\pi $$"}, {"identifier": "B", "content": "Attractive and equal to $$\\mu $$<sub>0</sub>I<sub>1</sub>I<sub>2</sub>/3$$\\pi $$"}, {"identifier": "C", "content": "Repulsive and equal to $$\\mu $$<sub>0</sub>I<sub>1<... | ["A"] | null | F<sub>3</sub> & F<sub>4</sub> cancel each other.<br><br>
Force on PQ will be F<sub>1</sub> = I<sub>2</sub>B<sub>1</sub> a<br><br>
= $${I_2}{{{\mu _0}{I_1}} \over {2\pi a}}a$$<br><br>
= $${{{\mu _0}{I_1}} \over {2\pi a}}a = {{{\mu _0}{I_1}{I_2}} \over {2\pi }}$$<br><br>
Force on RS will be F<sub>2</sub> = I<sub>2</s... | mcq | jee-main-2019-online-9th-april-morning-slot | 11,884 |
seqhEB9BDu57xBsDYsWqi | physics | magnetics | force-and-torque-on-current-carrying-conductor | A thin strip 10 cm long is on a U shaped wire
of negligible resistance and it is connected to
a spring of spring constant 0.5 Nm<sup>–1</sup>
(see figure). The assembly is kept in a uniform
magnetic field of 0.1 T. If the strip is pulled
from its equilibrium position and released, the
number of oscillation it performs... | [{"identifier": "A", "content": "50000"}, {"identifier": "B", "content": "1000"}, {"identifier": "C", "content": "5000"}, {"identifier": "D", "content": "10000"}] | ["C"] | null | <p>There are two forces on slider.</p>
<p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l36rep7l/ea20cd35-5aa5-4de5-8307-038452e786c0/2747e910-d402-11ec-b808-5752a3163b13/file-1l36rep7m.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l36rep7l/ea20cd35-5aa5-4de5-8307-038452e786... | mcq | jee-main-2019-online-8th-april-morning-slot | 11,885 |
TsixCqbp2jAzncJxD07k9k2k5l2kg1k | physics | magnetics | force-and-torque-on-current-carrying-conductor | A small circular loop of conducting wire has
radius a and carries current I. It is placed in a
uniform magnetic field B perpendicular to its
plane such that when rotated slightly about its
diameter and released, it starts performing
simple harmonic motion of time period T. If the
mass of the loop is m then : | [{"identifier": "A", "content": "$$T = \\sqrt {{{2m} \\over {IB}}} $$"}, {"identifier": "B", "content": "$$T = \\sqrt {{{\\pi m} \\over {IB}}} $$"}, {"identifier": "C", "content": "$$T = \\sqrt {{{\\pi m} \\over {2IB}}} $$"}, {"identifier": "D", "content": "$$T = \\sqrt {{{2\\pi m} \\over {IB}}} $$"}] | ["D"] | null | $$\tau $$ = - MBsin $$\theta $$
<br><br>I$$\alpha $$ = - MBsin $$\theta $$
<br><br>for small $$\theta $$,
<br><br>$$\alpha $$ = $$ - {{MB} \over I}\theta $$
<br><br>$$ \therefore $$ $${\omega ^2}$$ = $${{MB} \over I}$$
<br><br>$$ \Rightarrow $$ $$\omega $$ = $$\sqrt {{{I\left( {\pi {R^2}} \right)B} \over {{{m{R^2}} \ov... | mcq | jee-main-2020-online-9th-january-evening-slot | 11,887 |
z0jSA3ydEFG2cbKV67jgy2xukf15ar28 | physics | magnetics | force-and-torque-on-current-carrying-conductor | A charged particle carrying charge 1 $$\mu $$C is moving<br/> with velocity $$\left( {2\widehat i + 3\widehat j + 4\widehat k} \right)$$ ms<sup>–1</sup>. If an external
<br/>magnetic field of $$\left( {5\widehat i + 3\widehat j - 6\widehat k} \right)$$× 10<sup>–3</sup> T exists in the region where the particle is movin... | [{"identifier": "A", "content": "$${ - 0.30\\widehat i + 0.32\\widehat j - 0.09\\widehat k}$$"}, {"identifier": "B", "content": "$${ - 300\\widehat i + 320\\widehat j - 90\\widehat k}$$"}, {"identifier": "C", "content": "$${ - 30\\widehat i + 32\\widehat j - 9\\widehat k}$$"}, {"identifier": "D", "content": "$${ - 3.0\... | ["C"] | null | Given,
<br><br>$${\overrightarrow V }$$ = $$\left( {2\widehat i + 3\widehat j + 4\widehat k} \right)$$ ms<sup>–1</sup>
<br><br>$${\overrightarrow B }$$ = $$\left( {5\widehat i + 3\widehat j - 6\widehat k} \right)$$× 10<sup>–3</sup> T
<br><br>q = 1 $$\mu $$C
<br><br>$$\overrightarrow F = q\left( {\overrightarrow V \ti... | mcq | jee-main-2020-online-3rd-september-morning-slot | 11,888 |
w7TJS3KDVAdtQBc94fjgy2xukfganc8b | physics | magnetics | force-and-torque-on-current-carrying-conductor | A square loop of side 2$$a$$, and carrying current
I, is kept in XZ plane with its centre at origin.
A long wire carrying the same current I is
placed parallel to the z-axis and passing
through the point (0, b, 0), (b >> a). The
magnitude of the torque on the loop about zaxis is given by : | [{"identifier": "A", "content": "$${{2{\\mu _0}{I^2}{a^2}} \\over {\\pi b}}$$"}, {"identifier": "B", "content": "$${{{\\mu _0}{I^2}{a^2}} \\over {2\\pi b}}$$"}, {"identifier": "C", "content": "$${{{\\mu _0}{I^2}{a^3}} \\over {2\\pi {b^2}}}$$"}, {"identifier": "D", "content": "$${{2{\\mu _0}{I^2}{a^3}} \\over {\\pi {b^2... | ["A"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734263892/exam_images/pdkzbcfy2zsqculg9f8m.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 5th September Morning Slot Physics - Magnetic Effect of Current Question 117 English Explanation">... | mcq | jee-main-2020-online-5th-september-morning-slot | 11,889 |
ATIiDeCu8dxdAfjFxA1kmkrlf0y | physics | magnetics | force-and-torque-on-current-carrying-conductor | A loop of flexible wire of irregular shape carrying current is placed in an external magnetic field. Identify the effect of the field on the wire. | [{"identifier": "A", "content": "Loop assumes circular shape with its plane normal to the field."}, {"identifier": "B", "content": "Loop assumes circular shape with its plane parallel to the field."}, {"identifier": "C", "content": "Wire gets stretched to become straight."}, {"identifier": "D", "content": "Shape of the... | ["A"] | null | Force on each wire be along radially outward and equal so, it will take the shape of circle and
parallel to the field. | mcq | jee-main-2021-online-18th-march-morning-shift | 11,891 |
1ktbvnckg | physics | magnetics | force-and-torque-on-current-carrying-conductor | A coil in the shape of an equilateral triangle of side 10 cm lies in a vertical plane between the pole pieces of permanent magnet producing a horizontal magnetic field 20 mT. The torque acting on the coil when a current of 0.2 A is passed through it and its plane becomes parallel to the magnetic field will be $$\sqrt x... | [] | null | 3 | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734264258/exam_images/sesxtfmgyuda8gauksnh.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 26th August Evening Shift Physics - Magnetic Effect of Current Question 98 English Explanation"> <... | integer | jee-main-2021-online-26th-august-evening-shift | 11,892 |
1l55k8zrb | physics | magnetics | force-and-torque-on-current-carrying-conductor | <p>Two parallel, long wires are kept 0.20 m apart in vacuum, each carrying current of x A in the same direction. If the force of attraction per meter of each wire is 2 $$\times$$ 10<sup>$$-$$6</sup> N, then the value of x is approximately :</p> | [{"identifier": "A", "content": "1"}, {"identifier": "B", "content": "2.4"}, {"identifier": "C", "content": "1.4"}, {"identifier": "D", "content": "2"}] | ["C"] | null | <p>$${{dF} \over {dl}} = 2 \times {10^{ - 6}}$$ N/m $$ = {{{\mu _0}{i_1}{i_2}} \over {2\pi d}}$$</p>
<p>$$2 \times {10^{ - 6}} = {{2 \times {{10}^{ - 7}} \times {x^2}} \over {0.2}}$$</p>
<p>$$x = \sqrt 2 \simeq 1.4$$</p> | mcq | jee-main-2022-online-28th-june-evening-shift | 11,894 |
1l58ilx70 | physics | magnetics | force-and-torque-on-current-carrying-conductor | <p>Two 10 cm long, straight wires, each carrying a current of 5A are kept parallel to each other. If each wire experienced a force of 10<sup>$$-$$5</sup> N, then separation between the wires is ____________ cm.</p> | [] | null | 5 | <p>$${{dF} \over {dl}} = {{{\mu _0}{i_1}{i_2}} \over {2\pi d}}$$</p>
<p>So $${{2 \times {{10}^{ - 7}} \times 5 \times 5} \over d} = {{{{10}^{ - 5}}} \over {10 \times {{10}^{ - 2}}}}$$</p>
<p>$$d = {{2 \times {{10}^{ - 7}} \times 5 \times 5} \over {{{10}^{ - 4}}}}$$</p>
<p>= 50 mm</p>
<p>= 5 cm</p> | integer | jee-main-2022-online-26th-june-evening-shift | 11,895 |
1l5c2otts | physics | magnetics | force-and-torque-on-current-carrying-conductor | <p>Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R).</p>
<p>Assertion (A) : In an uniform magnetic field, speed and energy remains the same for a moving charged particle.</p>
<p>Reason (R) : Moving charged particle experiences magnetic force perpendicular to its ... | [{"identifier": "A", "content": "Both (A) and (R) are true and (R) is the correct explanation of (A)."}, {"identifier": "B", "content": "Both (A) and (R) are true but (R) is NOT the correct explanation of (A)."}, {"identifier": "C", "content": "(A) is true but (R) is false."}, {"identifier": "D", "content": "(A) is fal... | ["A"] | null | <p>Magnetic force $$\overrightarrow F \bot \overrightarrow v $$</p>
<p>$$ \Rightarrow {W_b} = 0$$</p>
<p>$$ \Rightarrow \Delta KE = 0$$ and speed remains constant.</p> | mcq | jee-main-2022-online-24th-june-morning-shift | 11,897 |
1l6dyoqw4 | physics | magnetics | force-and-torque-on-current-carrying-conductor | <p>Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is $$6: 5$$ and their respective masses ratio is $$9: 4$$. Then, the ratio of their charges will be :</p> | [{"identifier": "A", "content": "8 : 5"}, {"identifier": "B", "content": "5 : 4"}, {"identifier": "C", "content": "5 : 3"}, {"identifier": "D", "content": "8 : 7"}] | ["B"] | null | <p>We know that $$R = {{mv} \over {Bq}} = \sqrt {{{2mK} \over {Bq}}} $$</p>
<p>$$\Rightarrow$$ Ratio of radii $$ = {{{R_1}} \over {{R_2}}} = \sqrt {{{{m_1}} \over {{m_2}}}} {{{q_2}} \over {{q_1}}}$$</p>
<p>$$ \Rightarrow {6 \over 5} = \sqrt {{9 \over 4}} {{{q_2}} \over {{q_1}}}$$</p>
<p>$$ \Rightarrow {{{q_1}} \over {{... | mcq | jee-main-2022-online-25th-july-morning-shift | 11,898 |
1l6gmheed | physics | magnetics | force-and-torque-on-current-carrying-conductor | <p>A charge particle is moving in a uniform magnetic field $$(2 \hat{i}+3 \hat{j}) \,\mathrm{T}$$. If it has an acceleration of $$(\alpha \hat{i}-4 \hat{j})\, \mathrm{m} / \mathrm{s}^{2}$$, then the value of $$\alpha$$ will be :</p> | [{"identifier": "A", "content": "3"}, {"identifier": "B", "content": "6"}, {"identifier": "C", "content": "12"}, {"identifier": "D", "content": "2"}] | ["B"] | null | <p>As magnetic force is perpendicular to magnetic field</p>
<p>So, $$\overrightarrow F $$ . $$\overrightarrow B $$ must be 0</p>
<p>So, 2$$\alpha$$ $$-$$ 12 = 0</p>
<p>$$\alpha$$ = 6</p> | mcq | jee-main-2022-online-26th-july-morning-shift | 11,899 |
1l6kneiyi | physics | magnetics | force-and-torque-on-current-carrying-conductor | <p>A cyclotron is used to accelerate protons. If the operating magnetic field is $$1.0 \mathrm{~T}$$ and the radius of the cyclotron 'dees' is $$60 \mathrm{~cm}$$, the kinetic energy of the accelerated protons in MeV will be :</p>
<p>$$[\mathrm{use} \,\,\mathrm{m}_{\mathrm{p}}=1.6 \times 10^{-27} \mathrm{~kg}, \mathrm{... | [{"identifier": "A", "content": "12"}, {"identifier": "B", "content": "18"}, {"identifier": "C", "content": "16"}, {"identifier": "D", "content": "32"}] | ["B"] | null | <p>$$R = {{mv} \over {Bq}} = {{\sqrt {2mK} } \over {Bq}}$$</p>
<p>$$ \Rightarrow K = {{{B^2}{q^2}{R^2}} \over {2m}}$$</p>
<p>$$ = {{{{(1.6 \times {{10}^{ - 19}})}^2} \times {{0.6}^2}} \over {2 \times 1.6 \times {{10}^{ - 27}}}}$$ J</p>
<p>$$= 18$$ MeV</p> | mcq | jee-main-2022-online-27th-july-evening-shift | 11,900 |
1l6nslh5v | physics | magnetics | force-and-torque-on-current-carrying-conductor | <p>A triangular shaped wire carrying $$10 \mathrm{~A}$$ current is placed in a uniform magnetic field of $$0.5 \mathrm{~T}$$, as shown in figure. The magnetic force on segment $$\mathrm{CD}$$ is</p>
<p>(Given $$\mathrm{BC}=\mathrm{CD}=\mathrm{BD}=5 \mathrm{~cm}$$.)</p>
<p><img src="data:image/png;base64,UklGRpQJAABXRUJ... | [{"identifier": "A", "content": "0.126 N"}, {"identifier": "B", "content": "0.312 N"}, {"identifier": "C", "content": "0.216 N"}, {"identifier": "D", "content": "0.245 N"}] | ["C"] | null | <p>$$\overrightarrow F = i\overrightarrow l \times \overrightarrow B $$</p>
<p>$$ = ilB\sin 60^\circ $$</p>
<p>$$ = 10 \times {5 \over {100}} \times 0.5 \times {{\sqrt 3 } \over 2}$$</p>
<p>$$ = 0.2165$$ N</p> | mcq | jee-main-2022-online-28th-july-evening-shift | 11,902 |
1l6rgtjxx | physics | magnetics | force-and-torque-on-current-carrying-conductor | <p>A wire X of length $$50 \mathrm{~cm}$$ carrying a current of $$2 \mathrm{~A}$$ is placed parallel to a long wire $$\mathrm{Y}$$ of length $$5 \mathrm{~m}$$. The wire $$\mathrm{Y}$$ carries a current of $$3 \mathrm{~A}$$. The distance between two wires is $$5 \mathrm{~cm}$$ and currents flow in the same direction. Th... | [{"identifier": "A", "content": "$$1.2 \\times 10^{-5} \\mathrm{~N}$$ directed towards wire $$\\mathrm{X}$$."}, {"identifier": "B", "content": "$$1.2 \\times 10^{-4} \\mathrm{~N}$$ directed away from wire $$\\mathrm{X}$$."}, {"identifier": "C", "content": "$$1.2 \\times 10^{-4} \\mathrm{~N}$$ directed towards wire $$\\... | ["A"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l7e980jx/74287a5b-9bac-4113-b5cb-b03b67df1fb8/2bc3b0c0-2752-11ed-a077-1f1e3989e798/file-1l7e980jy.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l7e980jx/74287a5b-9bac-4113-b5cb-b03b67df1fb8/2bc3b0c0-2752-11ed-a077-1f1e3989e798... | mcq | jee-main-2022-online-29th-july-evening-shift | 11,903 |
ldqvvzd6 | physics | magnetics | force-and-torque-on-current-carrying-conductor | <p>A current carrying rectangular loop PQRS is made of uniform wire. The length $P R=Q S=5 \mathrm{~cm}$ and $P Q=R S=100 \mathrm{~cm}$. If ammeter current reading changes from I to $2 I$, the ratio of magnetic forces per unit length on the wire $P Q$ due to wire $R S$ in the two cases respectively $\left(f_{P Q}^I: f_... | [{"identifier": "A", "content": "1 : 4"}, {"identifier": "B", "content": "1 : 3"}, {"identifier": "C", "content": "1 : 2"}, {"identifier": "D", "content": "1 : 5"}] | ["A"] | null | <p>Force between two current carrying wire</p>
<p>$$ = {{{\mu _0}{I_1}{I_2}} \over {2\pi d}} \times L$$</p>
<p>Here, $${I_1}$$ & $${I_2}$$ are equal</p>
<p>$$F = {{{\mu _0}{I^2}} \over {2\pi d}} \times L$$</p>
<p>$$F \propto {I^2}$$</p>
<p>$${{{F_I}} \over {{F_{2I}}}} = {{{I^2}} \over {4{I^2}}} = {1 \over 4}$$</p> | mcq | jee-main-2023-online-30th-january-evening-shift | 11,905 |
1ldr0sqbd | physics | magnetics | force-and-torque-on-current-carrying-conductor | <p>A massless square loop, of wire of resistance $$10 \Omega$$, supporting a mass of $$1 \mathrm{~g}$$, hangs vertically with one of its sides in a uniform magnetic field of $$10^{3} \mathrm{G}$$, directed outwards in the shaded region. A dc voltage $$\mathrm{V}$$ is applied to the loop. For what value of $$\mathrm{V}$... | [{"identifier": "A", "content": "1 V"}, {"identifier": "B", "content": "$$\\frac{1}{10}$$V"}, {"identifier": "C", "content": "10 V"}, {"identifier": "D", "content": "100 V"}] | ["C"] | null | For balancing of force</p>
<p>$$\therefore F_{loop}=\mathrm{weight}$$</p>
<p>$$\left( {{V \over R}} \right)IB = mg$$</p>
<p>$$\left( {{V \over {10}}} \right) \times {{10} \over {100}} \times ({10^3} \times {10^{ - 4}}) = \left( {{1 \over {1000}}} \right) \times 10$$</p>
<p>$$V = 10$$ volts</p> | mcq | jee-main-2023-online-30th-january-morning-shift | 11,906 |
1ldws6scp | physics | magnetics | force-and-torque-on-current-carrying-conductor | <p>A single turn current loop in the shape of a right angle triangle with sides 5 cm, 12 cm, 13 cm is carrying a current of 2 A. The loop is in a uniform magnetic field of magnitude 0.75 T whose direction is parallel to the current in the 13 cm side of the loop. The magnitude of the magnetic force on the 5 cm side will... | [] | null | 9 | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1le4czquh/15c84f5c-6f3c-4603-a917-b7f2dbe9ff69/9777e990-ac76-11ed-aaa5-ebe03f1bac28/file-1le4czqui.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1le4czquh/15c84f5c-6f3c-4603-a917-b7f2dbe9ff69/9777e990-ac76-11ed-aaa5-ebe03f1bac28... | integer | jee-main-2023-online-24th-january-evening-shift | 11,907 |
1ldydajd8 | physics | magnetics | force-and-torque-on-current-carrying-conductor | <p>Two long straight wires P and Q carrying equal current 10A each were kept parallel to each other at 5 cm distance. Magnitude of magnetic force experienced by 10 cm length of wire P is F$$_1$$. If distance between wires is halved and currents on them are doubled, force F$$_2$$ on 10 cm length of wire P will be:</p> | [{"identifier": "A", "content": "$$\\frac{F_1}{8}$$"}, {"identifier": "B", "content": "10 F$$_1$$"}, {"identifier": "C", "content": "$$\\frac{F_1}{10}$$"}, {"identifier": "D", "content": "8 F$$_1$$"}] | ["D"] | null | $$
\begin{aligned}
& \text { Force per unit length between two parallel straight wires }=\frac{\mu_0 \mathrm{i}_1 \mathrm{i}_2}{2 \pi \mathrm{d}} \\\\
& \frac{\mathrm{F}_1}{\mathrm{~F}_2}=\frac{\frac{\mu_0(10)^2}{2 \pi(5 \mathrm{~cm})}}{\frac{\mu_0(20)^2}{2 \pi\left(\frac{5 \mathrm{~cm}}{2}\right)}}=\frac{1}{8} \\\\
& ... | mcq | jee-main-2023-online-24th-january-morning-shift | 11,908 |
1lgp0hliq | physics | magnetics | force-and-torque-on-current-carrying-conductor | <p>An electron is moving along the positive $$\mathrm{x}$$-axis. If the uniform magnetic field is applied parallel to the negative z-axis, then</p>
<p>A. The electron will experience magnetic force along positive y-axis</p>
<p>B. The electron will experience magnetic force along negative y-axis</p>
<p>C. The electron w... | [{"identifier": "A", "content": "A and E only"}, {"identifier": "B", "content": "B and D only"}, {"identifier": "C", "content": "B and E only"}, {"identifier": "D", "content": "C and D only"}] | ["C"] | null | The Lorentz force equation is given as:
<br/><br/>
$$\vec{F} = -q(\vec{v} \times \vec{B})$$
<br/><br/>
The electron is moving along the positive x-axis, so its velocity vector is $$\vec{v} = v_x \hat{i}$$. The magnetic field is applied parallel to the negative z-axis, so its magnetic field vector is $$\vec{B} = -B_z \h... | mcq | jee-main-2023-online-13th-april-evening-shift | 11,909 |
1lgp0xzx8 | physics | magnetics | force-and-torque-on-current-carrying-conductor | <p>A straight wire $$\mathrm{AB}$$ of mass $$40 \mathrm{~g}$$ and length $$50 \mathrm{~cm}$$ is suspended by a pair of flexible leads in uniform magnetic field of magnitude $$0.40 \mathrm{~T}$$ as shown in the figure. The magnitude of the current required in the wire to remove the tension in the supporting leads is ___... | [] | null | 2 | In the given situation, the wire is suspended by a pair of flexible leads in a uniform magnetic field. Due to the magnetic field, the wire experiences a magnetic force which causes it to hang at an angle to the vertical. The tension in the flexible leads provides the restoring force to balance the weight of the wire.
... | integer | jee-main-2023-online-13th-april-evening-shift | 11,910 |
1lgswj9wf | physics | magnetics | force-and-torque-on-current-carrying-conductor | <p>An electron is allowed to move with constant velocity along the axis of current carrying straight solenoid.</p>
<p>A. The electron will experience magnetic force along the axis of the solenoid.</p>
<p>B. The electron will not experience magnetic force.</p>
<p>C. The electron will continue to move along the axis of t... | [{"identifier": "A", "content": "B, C and D only"}, {"identifier": "B", "content": "B and C only"}, {"identifier": "C", "content": "A and D only"}, {"identifier": "D", "content": "B and E only"}] | ["B"] | null | <p>The magnetic field inside a solenoid is uniform and parallel to the axis of the solenoid. When an electron moves with constant velocity along the axis of the solenoid, the angle between its velocity vector and the magnetic field is 0°.</p>
<p>The magnetic force experienced by a moving charge is given by the Lorentz ... | mcq | jee-main-2023-online-11th-april-evening-shift | 11,911 |
jaoe38c1lsd5orfk | physics | magnetics | force-and-torque-on-current-carrying-conductor | <p>A uniform magnetic field of $$2 \times 10^{-3} \mathrm{~T}$$ acts along positive $$Y$$-direction. A rectangular loop of sides $$20 \mathrm{~cm}$$ and $$10 \mathrm{~cm}$$ with current of $$5 \mathrm{~A}$$ is in $$Y-Z$$ plane. The current is in anticlockwise sense with reference to negative $$X$$ axis. Magnitude and d... | [{"identifier": "A", "content": "$$2 \\times 10^{-4} \\mathrm{~N}$$- $$\\mathrm{m}$$ along negative $$Z$$-direction\n"}, {"identifier": "B", "content": "$$2 \\times 10^{-4} \\mathrm{~N}$$ - $$\\mathrm{m}$$ along positive $$X$$-direction\n"}, {"identifier": "C", "content": "$$2 \\times 10^{-4} \\mathrm{~N}$$ - $$\\mathr... | ["A"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lsiipawi/c2ee55fb-a339-4a52-9686-5e1d94c5e2cf/ec3b7520-c96a-11ee-b416-eff853096672/file-6y3zli1lsiipawj.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/6y3zli1lsiipawi/c2ee55fb-a339-4a52-9686-5e1d94c5e2cf/ec3b7520-c96a-11ee... | mcq | jee-main-2024-online-31st-january-evening-shift | 11,912 |
jaoe38c1lse6aaap | physics | magnetics | force-and-torque-on-current-carrying-conductor | <p>A rigid wire consists of a semicircular portion of radius $$R$$ and two straight sections. The wire is partially immerged in a perpendicular magnetic field $$B=B_0 \hat{k}$$ as shown in figure. The magnetic force on the wire if it has a current $$i$$ is:</p>
<p><img src="data:image/png;base64,UklGRs4aAABXRUJQVlA4IMI... | [{"identifier": "A", "content": "$$i B R \\hat{j}$$\n"}, {"identifier": "B", "content": "$$-2 i B R \\hat{j}$$\n"}, {"identifier": "C", "content": "$$2 i B R \\hat{j}$$\n"}, {"identifier": "D", "content": "$$-i B R \\hat{j}$$"}] | ["B"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lsludpk4/453b8c51-df9f-4c63-8827-ba1780cacc92/f1578640-cb3e-11ee-ad47-a16d1086e690/file-6y3zli1lsludpk5.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/6y3zli1lsludpk4/453b8c51-df9f-4c63-8827-ba1780cacc92/f1578640-cb3e-11ee... | mcq | jee-main-2024-online-31st-january-morning-shift | 11,913 |
lv0vyunc | physics | magnetics | force-and-torque-on-current-carrying-conductor | <p>The magnetic field existing in a region is given by $$\vec{B}=0.2(1+2 x) \hat{k}$$. A square loop of edge $$50 \mathrm{~cm}$$ carrying 0.5 A current is placed in $$x$$-$$y$$ plane with its edges parallel to the $$x$$-$$y$$ axes, as shown in figure. The magnitude of the net magnetic force experienced by the loop is _... | [] | null | 50 | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1lwkghan2/c22e233b-e1c8-4f55-b514-e4864536fccf/aa1cd3e0-19ac-11ef-9bb2-3724c2e449d4/file-1lwkghan3.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1lwkghan2/c22e233b-e1c8-4f55-b514-e4864536fccf/aa1cd3e0-19ac-11ef-9bb2-3724c2e449d4... | integer | jee-main-2024-online-4th-april-morning-shift | 11,915 |
lv5gt4pj | physics | magnetics | force-and-torque-on-current-carrying-conductor | <p>A square loop PQRS having 10 turns, area $$3.6 \times 10^{-3} \mathrm{~m}^2$$ and resistance $$100 \Omega$$ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude $$\mathrm{B}=0.5 \mathrm{~T}$$ as shown. Work done in pulling the loop out of the field in $$1.0 \mathrm{~s}$$ is _________ $$\... | [] | null | 3 | <p>$$\begin{aligned}
& A = 36 \times 10^{-4} \mathrm{~m}^2 \\
& I= 6 \times 10^{-2} \mathrm{~m} \\
& =6 \mathrm{~cm} \\
V & =\frac{6 \mathrm{~cm}}{1 \mathrm{sec}}=6 \mathrm{~cm} / \mathrm{s} \\
\varepsilon & =B / \mathrm{vn}^2=0.5 \times \frac{6}{100} \times \frac{6}{100} \\
& =18 \times 10^{-4} \mathrm{~V} \\
E & =\fr... | integer | jee-main-2024-online-8th-april-morning-shift | 11,916 |
1lgq23whb | physics | magnetics | magnetic-field-of-moving-charge | <p>The source of time varying magnetic field may be</p>
<p>(A) a permanent magnet</p>
<p>(B) an electric field changing linearly with time</p>
<p>(C) direct current</p>
<p>(D) a decelerating charge particle</p>
<p>(E) an antenna fed with a digital signal</p>
<p>Choose the correct answer from the options given below:</p... | [{"identifier": "A", "content": "(D) only"}, {"identifier": "B", "content": "(A) only"}, {"identifier": "C", "content": "(B) and (D) only"}, {"identifier": "D", "content": "(C) and (E) only"}] | ["A"] | null | Source of time varying magnetic field may be<br/><br/>
$\rightarrow$ accelerated or retarded charge which produces varying electric and magnetic fields.<br/><br/>
$\rightarrow$ An electric field varying linearly with time will not produce variable magnetic field as current will be constant | mcq | jee-main-2023-online-13th-april-morning-shift | 11,918 |
1lh016ns7 | physics | magnetics | magnetic-field-of-moving-charge | <p>A charge particle moving in magnetic field B, has the components of velocity along B as well as perpendicular to B. The path of the charge particle will be</p> | [{"identifier": "A", "content": "helical path with the axis along magnetic field $$\\mathrm{B}$$"}, {"identifier": "B", "content": "straight along the direction of magnetic field $$\\mathrm{B}$$"}, {"identifier": "C", "content": "circular path"}, {"identifier": "D", "content": "helical path with the axis perpendicular ... | ["A"] | null | <p>When a charged particle moves in a magnetic field, its motion is affected by the components of its velocity that are parallel and perpendicular to the magnetic field.</p>
<ol>
<li><p>The component of velocity that is parallel to the magnetic field doesn't get affected by the magnetic field. It causes the particl... | mcq | jee-main-2023-online-8th-april-morning-shift | 11,919 |
1lh31li4v | physics | magnetics | magnetic-field-of-moving-charge | <p>A proton with a kinetic energy of $$2.0 ~\mathrm{eV}$$ moves into a region of uniform magnetic field of magnitude $$\frac{\pi}{2} \times 10^{-3} \mathrm{~T}$$. The angle between the direction of magnetic field and velocity of proton is $$60^{\circ}$$. The pitch of the helical path taken by the proton is __________ $... | [] | null | 40 | <p>Given a proton with a kinetic energy of 2 eV, moving into a region of uniform magnetic field of magnitude $$\frac{\pi}{2} \times 10^{-3} T$$, and with an angle of $$60^{\circ}$$ between the direction of the magnetic field and the velocity of the proton, we want to determine the pitch of the helical path taken by the... | integer | jee-main-2023-online-6th-april-evening-shift | 11,920 |
EyqEBAMhZ9COVcq4 | physics | magnetics | magnetic-moment | <p>A rectangular loop of sides $$10$$ $$cm$$ and $$5$$ $$cm$$ carrying a current $$1$$ of $$12A$$ is placed in different orientations as shown in the figures below :</p>
<p><img src="data:image/png;base64,UklGRnALAABXRUJQVlA4IGQLAABwhgCdASpZAQADP4G812Y2LqwnIPGZasAwCWlu8p8d1r+CN+fb5w/WzvJyF7Ovs73Z92o3152NAH7BZvDxf/z53vv... | [{"identifier": "A", "content": "$$(B)$$ and $$(D)$$, respectively"}, {"identifier": "B", "content": "$$(B)$$ and $$(C)$$, respectively"}, {"identifier": "C", "content": "$$(A)$$ and $$(B)$$, respectively"}, {"identifier": "D", "content": "$$(A)$$ and $$(C)$$, respectively"}] | ["A"] | null | For stable equilibrium $$\mathop M\limits^ \to ||\mathop B\limits^ \to $$
<br><br>For unstable equilibrium $$\mathop M\limits^ \to ||\left( { - \mathop B\limits^ \to } \right)$$ | mcq | jee-main-2015-offline | 11,921 |
oJqaOE9TjfnZrMmEPPXr2 | physics | magnetics | magnetic-moment | A charge q is spread uniformly over an insulated loop of radius r. If it is rotated with an angular velocity $$\omega $$ with resect to normal axis then the magnetic moment of the loop is : | [{"identifier": "A", "content": "q $$\\omega $$r<sup>2</sup>"}, {"identifier": "B", "content": "$${4 \\over 3}$$ q $$\\omega $$r<sup>2</sup>"}, {"identifier": "C", "content": "$${3 \\over 2}$$ q $$\\omega $$r<sup>2</sup>"}, {"identifier": "D", "content": "$${1 \\over 2}$$ q $$\\omega $$r<sup>2</sup>"}] | ["D"] | null | Magnetic moment,
<br><br>$$\mu $$ = I A
<br><br>= $${q \over T}\left( {\pi {r^2}} \right)$$
<br><br>= $${q \over {2\pi /\omega }}\left( {\pi {r^2}} \right)$$
<br><br>= $${{qw} \over {2\pi }}$$ $$\left( {\pi {r^2}} \right)$$
<br><br>= $${1 \over 2}$$ q$$\omega $$r<sup>2</sup> | mcq | jee-main-2018-online-16th-april-morning-slot | 11,922 |
DWnCemVRIjYUnDTsgPP9j | physics | magnetics | magnetic-moment | An insulating thin rod of length $$l$$ has a linear charge density $$\rho \left( x \right)$$ = $${\rho _0}{x \over l}$$ on it. The rod is rotated about an axis passing through the origin (x = 0) and perpendicular to the rod. If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is - | [{"identifier": "A", "content": "$${\\pi \\over 3}n\\rho {l^3}$$"}, {"identifier": "B", "content": "$${\\pi \\over 4}n\\rho {l^3}$$"}, {"identifier": "C", "content": "$$n\\rho {l^3}$$ "}, {"identifier": "D", "content": "$$\\pi n\\rho {l^3}$$"}] | ["B"] | null | $$ \because $$ M = NIA
<br><br>dq = $$\lambda $$dx & A = $$\pi $$x<sup>2</sup>
<br><br>$$\int {dm} = \int {\left( x \right){{{\rho _0}x} \over \ell }} \,dx.\pi {x^2}$$
<br><br>M = $${{n{\rho _0}\pi } \over \ell }.\int\limits_0^\ell {{x^3}.dx} = {{n{\rho _0}\pi } \over \ell }.\l... | mcq | jee-main-2019-online-10th-january-morning-slot | 11,923 |
zctkNho8M3hSAoizBFZkd | physics | magnetics | magnetic-moment | A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their magnetic moment parallel to their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in a uniform magnetic field in such a manner that their magnetic moments make a small an... | [{"identifier": "A", "content": "T<sub>h</sub> = 1.5 T<sub>c</sub>"}, {"identifier": "B", "content": "T<sub>h</sub> = T<sub>c</sub> "}, {"identifier": "C", "content": "T<sub>h</sub> = 2T<sub>c</sub> "}, {"identifier": "D", "content": "T<sub>h</sub> = 0.5 T<sub>c</sub>"}] | ["B"] | null | T = $$2\pi \sqrt {{1 \over {\mu B}}} $$
<br><br>T<sub>h</sub> = $$2\pi \sqrt {{{m{R^2}} \over {\left( {2\mu } \right)B}}} $$
<br><br>T<sub>C</sub> = $$2\pi \sqrt {{{1/2m{R^2}} \over {\mu B}}} $$ | mcq | jee-main-2019-online-10th-january-evening-slot | 11,924 |
PizvXf9IurDfSmeCbKck5 | physics | magnetics | magnetic-moment | A circular coil having N turns and radius r
carries a current I. It is held in the XZ plane in
a magnetic field B$${\mathop i\limits^ \wedge }$$ . The torque on the coil due
to the magnetic field is : | [{"identifier": "A", "content": "$${{B{r^2}I} \\over {\\pi N}}$$"}, {"identifier": "B", "content": "B$$\\pi $$r<sup>2</sup>IN"}, {"identifier": "C", "content": "Zero"}, {"identifier": "D", "content": "$${{B\\pi{r^2}I} \\over { N}}$$"}] | ["B"] | null | <p>According to the question, the situation can be drawn as</p>
<p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l331e86r/c052133d-ed72-466e-96c1-d00bafb15083/12d32430-d1f6-11ec-b83f-ebfea682138a/file-1l331e86s.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l331e86r/c052133d-... | mcq | jee-main-2019-online-8th-april-morning-slot | 11,925 |
R1fpR3Et0NXNzqMI3k3rsa0w2w9jwziets2 | physics | magnetics | magnetic-moment | A square loop is carrying a steady current I and the magnitude of its magnetic dipole moment is m. if this
square loop is changed to a circular loop and it carries the same current, the magnitude of the magnetic dipole
moment of circular loop will be: | [{"identifier": "A", "content": "$${m \\over \\pi }$$"}, {"identifier": "B", "content": "$${{3m} \\over \\pi }$$"}, {"identifier": "C", "content": "$${{2m} \\over \\pi }$$"}, {"identifier": "D", "content": "$${{4m} \\over \\pi }$$"}] | ["D"] | null | Let the given square loop has side $a$, then its magnetic dipole moment will be
<br><br>$$
m=I a^2
$$
<br><br>When square is converted into a circular loop of radius $r$,
<br><br><img src="https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lj670g6j/203e8b10-11ee-48e9-971d-90abd28ae946/da751bb0-1075-11ee-a86a-... | mcq | jee-main-2019-online-10th-april-evening-slot | 11,926 |
HGmKedilh1JT1A1XVnjgy2xukexwn6da | physics | magnetics | magnetic-moment | A wire carrying current I is bent in the shape
ABCDEFA as shown, where rectangle ABCDA
and ADEFA are perpendicular to each other. If
the sides of the rectangles are of lengths a and
b, then the magnitude and direction of
magnetic moment of the loop ABCDEFA is
<img src="data:image/png;base64,UklGRg4WAABXRUJQVlA4IAIWAADQ... | [{"identifier": "A", "content": "$$\\sqrt 2 $$abI, along $$\\left( {{{\\widehat j} \\over {\\sqrt 5 }} + {{2\\widehat k} \\over {\\sqrt 5 }}} \\right)$$"}, {"identifier": "B", "content": "abI, along $$\\left( {{{\\widehat j} \\over {\\sqrt 5 }} + {{2\\widehat k} \\over {\\sqrt 5 }}} \\right)$$"}, {"identifier": "C", "c... | ["C"] | null | For ABCD
<br><br>$${\overrightarrow M _1}$$ = abI$$\widehat k$$
<br><br>For DEFA
<br><br>$${\overrightarrow M _2}$$ = abI$$\widehat j$$
<br><br>$$\overrightarrow M = {\overrightarrow M _1} + {\overrightarrow M _2}$$
<br><br>= $$abI\left( {\widehat k + \widehat j} \right)$$
<br><br>= $$abI\sqrt 2 \left( {{{\widehat k} ... | mcq | jee-main-2020-online-2nd-september-evening-slot | 11,927 |
FIA4lmu30DoiGg7s2bjgy2xukfahce4k | physics | magnetics | magnetic-moment | A circular coil has moment of inertia 0.8 kg m<sup>2</sup>
around any diameter and is carrying current to
produce a magnetic moment of 20 Am<sup>2</sup>
. The coil is kept initially in a vertical position and it can
rotate freely around a horizontal diameter. When a uniform magnetic field of 4 T is applied along the
v... | [{"identifier": "A", "content": "10 $$\\pi $$ rad s<sup>\u20131</sup>"}, {"identifier": "B", "content": "20 $$\\pi $$ rad s<sup>\u20131</sup>"}, {"identifier": "C", "content": "$$10{\\left( 3 \\right)^{1/4}}$$ rad s<sup>\u20131</sup>"}, {"identifier": "D", "content": "20 rad s<sup>\u20131</sup>"}] | ["C"] | null | By energy conservation <br><br>U<sub>i</sub> + K<sub>i</sub> = U<sub>f</sub> + K<sub>f</sub><br><br>$$ \Rightarrow $$ $$ - MB\,\cos 90^\circ + 0 = - MB\,\cos 30^\circ + {1 \over 2}I{\omega ^2}$$<br><br>$$ \Rightarrow $$ $$MB{{\sqrt 3 } \over 2}$$ $$ = {1 \over 2}I{\omega ^2}$$<br><br>$$ \Rightarrow $$ $$\omega =$$$... | mcq | jee-main-2020-online-4th-september-evening-slot | 11,928 |
NHTCnOkEnWQEmeBkFljgy2xukfl3q9zw | physics | magnetics | magnetic-moment | An iron rod of volume 10<sup>–3</sup> m<sup>3</sup> and relative
permeability 1000 is placed as core in a
solenoid with 10 turns/cm. If a current of 0.5 A
is passed through the solenoid, then the
magnetic moment of the rod will be : | [{"identifier": "A", "content": "5 $$ \\times $$ 10<sup>2</sup> Am<sup>2</sup>"}, {"identifier": "B", "content": "0.5 $$ \\times $$ 10<sup>2</sup> Am<sup>2</sup>"}, {"identifier": "C", "content": "500 $$ \\times $$ 10<sup>2</sup> Am<sup>2</sup>"}, {"identifier": "D", "content": "50 $$ \\times $$ 10<sup>2</sup> Am<sup>2... | ["A"] | null | Given, V = 10<sup>–3</sup> m<sup>3</sup>
= Al
<br><br>I = 0.5A
<br><br>$$\mu $$<sub>r</sub> = 1000
<br><br>n = 10 turns/cm = $${{10} \over {{{10}^{ - 2}}}}$$ turn/m = 1000 turn/m
<br><br>Magnetic moment, M = NIA($$\mu $$<sub>r</sub> - 1)
<br><br>= (nl)IA($$\mu $$<sub>r</sub> - 1)
<br><br>= nI(Al)($$\mu $$<sub>r</sub> ... | mcq | jee-main-2020-online-5th-september-evening-slot | 11,929 |
7ex2GeeMpa163y6Q0Cjgy2xukg09scko | physics | magnetics | magnetic-moment | A charged particle going around in a circle can be considered to be a current loop. A particle of
mass m carrying charge q is moving in a plane with speed v under the influence of magnetic field $$\overrightarrow B $$.
The magnetic moment of this moving particle: | [{"identifier": "A", "content": "$${{m{v^2}\\overrightarrow B } \\over {2{B^2}}}$$"}, {"identifier": "B", "content": "-$${{m{v^2}\\overrightarrow B } \\over {2{B^2}}}$$"}, {"identifier": "C", "content": "-$${{m{v^2}\\overrightarrow B } \\over {{B^2}}}$$"}, {"identifier": "D", "content": "-$${{m{v^2}\\overrightarrow B }... | ["B"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266148/exam_images/k4zekbpfb54wdwqfvutq.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 6th September Evening Slot Physics - Magnetic Effect of Current Question 113 English Explanation">... | mcq | jee-main-2020-online-6th-september-evening-slot | 11,930 |
1ktagsd9j | physics | magnetics | magnetic-moment | Two short magnetic dipoles m<sub>1</sub> and m<sub>2</sub> each having magnetic moment of 1 Am<sup>2</sup> are placed at point O and P respectively. The distance between OP is 1 meter. The torque experienced by the magnetic dipole m<sub>2</sub> due to the presence of m<sub>1</sub> is ........... $$\times$$ 10<sup>$$-$$... | [] | null | 1 | $$\overrightarrow \tau = \overrightarrow {{M_2}} \times \overrightarrow {{B_1}} $$<br><br>$$\tau = {M_2}{B_1}\sin 90^\circ $$<br><br>$$ = 1 \times {{{\mu _0}} \over {4\pi }}{{{M_1}} \over {{{(1)}^3}}}1$$<br><br>= 10<sup>$$-$$7</sup> N.m | integer | jee-main-2021-online-26th-august-morning-shift | 11,931 |
1kte6z3bn | physics | magnetics | magnetic-moment | A uniform conducting wire of length is 24a, and resistance R is wound up as a current carrying coil in the shape of an equilateral triangle of side 'a' and then in the form of a square of side 'a'. The coil is connected to a voltage source V<sub>0</sub>. The ratio of magnetic moment of the coils in case of equilateral ... | [] | null | 3 | In triangle shape $${N_t} = {{24a} \over {3a}} = 8$$<br><br>In square $${N_s} = {{24a} \over {4a}} = 6$$<br><br>$${{{M_t}} \over {{M_3}}} = {{{N_t}I{A_t}} \over {{N_s}I{A_s}}}$$ [I will be same in both]<br><br>$$ = {{8 \times {{\sqrt 3 } \over 4} \times {a^2}} \over {6 \times {a^2}}}$$<br><br>$${{{M_t}} \over {{M_s}}} ... | integer | jee-main-2021-online-27th-august-morning-shift | 11,932 |
1ktjqdxfw | physics | magnetics | magnetic-moment | A long solenoid with 1000 turns/m has a core material with relative permeability 500 and volume 10<sup>3</sup> cm<sup>3</sup>. If the core material is replaced by another material having relative permeability of 750 with same volume maintaining same current of 0.75 A in the solenoid, the fractional change in the magnet... | [] | null | 250 | $${{\Delta M} \over M} = {{\Delta \mu } \over \mu } = {{250} \over {500}} = {1 \over 2}$$<br><br>$$ \Rightarrow $$ $${1 \over 2} = {x \over {499}} \Rightarrow x \simeq 250$$ | integer | jee-main-2021-online-31st-august-evening-shift | 11,933 |
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