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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&nbsp; =&nbsp; 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 &nbsp;=&nbsp; 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>$$ \therefore $$&nbsp;&nbsp;B<sub>0</sub> = $${{{\mu _0}i} \over {4\pi d}} + {{{\mu _0}i} \over {4\pi d}}$$ <br><br>or&nbsp;&nbsp;&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 )$$
mcq
jee-main-2021-online-17th-march-evening-shift
11,834
1kta8799v
physics
magnetics
biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire
The fractional change in the magnetic field intensity at a distance 'r' from centre on the axis of current carrying coil of radius 'a' to the magnetic field intensity at the centre of the same coil is : (Take r &lt; a)
[{"identifier": "A", "content": "$${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$$"}, {"identifier": "C", "content": "directly pro...
["C"]
null
<p>The magnetic field due to a current carrying wire can be calculated using Ampere&#39;s law. When the current is uniformly distributed across the cross-section of the wire, the situation will be different inside and outside the wire.</p> <p>Inside the wire (r &lt; a), the magnetic field is directly proportional to r ...
mcq
jee-main-2023-online-6th-april-morning-shift
11,862
1lh25y0ny
physics
magnetics
biot-savart's-law-and-magnetic-field-due-to-current-carrying-wire
<p>Two identical circular wires of radius $$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>$$ \therefore $$&nbsp;&nbsp;&nbsp;$$\tau $$<sub>1</sub> = $$\tau $$<sub>2</sub> <br><br>$$ \Rightarrow $$&nbsp;&nbsp;&nbsp;mB<sub>1</sub> sin$$\theta $$<sub>1</sub> = mB<sub>2</sub> sin$$\theta $$<sub>2</sub> <br><br>$$ \Rightarrow $$&nbsp;&nbsp;&nbsp...
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 $$<sub>0</sub>I<sub>1<...
["A"]
null
F<sub>3</sub> &amp; F<sub>4</sub> cancel each other.<br><br> Force on PQ will be F<sub>1</sub> = I<sub>2</sub>B<sub>1</sub> a<br><br> = $${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 &gt;&gt; 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}$$"}, {"identifier": "C", "content": "circular path"}, {"identifier": "D", "content": "helical path with the axis perpendicular ...
["A"]
null
<p>When a charged particle moves in a magnetic field, its motion is affected by the components of its velocity that are parallel and perpendicular to the magnetic field.</p> <ol> <li><p>The component of velocity that is parallel to the magnetic field doesn&#39;t get affected by the magnetic field. It causes the particl...
mcq
jee-main-2023-online-8th-april-morning-shift
11,919
1lh31li4v
physics
magnetics
magnetic-field-of-moving-charge
<p>A proton with a kinetic energy of $$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 $$ &nbsp;&nbsp;M = NIA <br><br>dq = $$\lambda $$dx&nbsp;&nbsp;&amp;&nbsp;&nbsp; A = $$\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