# JEE Main

Explore popular questions from Electromagnetic Induction and Alternating Currents for JEE Main. This collection covers Electromagnetic Induction and Alternating Currents previous year JEE Main questions hand picked by experienced teachers.

## Mathematics

Electromagnetic Induction and Alternating Currents

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Q 1. A rod of length {tex} \ell {/tex} is moved with a velocity {tex} v {/tex} in a magnetic field {tex} B {/tex} as shown in Fig., the equivalent electrical circuit is

A

B

D

##### Explanation

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Q 2. A varying magnetic flux linking a coil is given by {tex} \phi = x t ^ { 2 } . {/tex} If at a time {tex} t = 3 \mathrm { s } {/tex} , the EMF induced is 9{tex} \mathrm { V } {/tex} , then the value of {tex} x {/tex} is

A

0.66{tex} \mathrm { Wbs } ^ { - 2 } {/tex}

B

1.5{tex} \mathrm { Wbs } ^ { - 2 } {/tex}

C

{tex} - 0.66 \mathrm { Wbs } ^ { - 2 } {/tex}

{tex} - 1.5 \mathrm { Wbs } ^ { - 2 } {/tex}

##### Explanation

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Q 3. A conducting circular loop is placed in a uniform magnetic field of induction {tex} B {/tex} tesla with its plane normal to the field. Now the radius of the loop starts shrinking at the rate {tex} ( d r / d t ) {/tex} . Then the induced EMF at the instant when the radius is {tex} r {/tex} will be

A

{tex} \pi r B \left( \frac { d r } { d t } \right) {/tex}

2{tex} \pi r B \left( \frac { d r } { d t } \right) {/tex}

C

{tex} \pi r ^ { 2 } \left( \frac { d B } { d t } \right) {/tex}

D

{tex} B \frac { \pi r ^ { 2 } } { 2 } \frac { d r } { d t } {/tex}

##### Explanation

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Q 4. If the flux of magnetic induction through a coil of resistance {tex} R {/tex} and having {tex} n {/tex} turns changes from {tex} \phi _ { 1 }{/tex} to {tex} \phi _ { 2 } , {/tex} then the magnitude of the charge that passes through the coil is

A

{tex} \frac { \left( \phi _ { 2 } - \phi _ { 1 } \right) } { R } {/tex}

{tex} \frac { n \left( \phi _ { 2 } - \phi _ { 1 } \right) } { R } {/tex}

C

{tex} \frac { \left( \phi _ { 2 } - \phi _ { 1 } \right) } { n R } {/tex}

D

{tex} \frac { n R } { \left( \phi _ { 2 } - \phi _ { 1 } \right) } {/tex}

##### Explanation

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Q 5. A varying magnetic flux linking a coil is given by {tex} \phi = 3 t ^ { 2 } {/tex} . The magnitude of induced EMF in the loop at {tex} t = 3 \mathrm { s } {/tex} is

A

3{tex} \mathrm { V } {/tex}

B

9{tex} \mathrm { V } {/tex}

18{tex} \mathrm { V } {/tex}

D

27{tex} \mathrm { V } {/tex}

##### Explanation

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Q 6. A horizontal telegraph wire 0.5 km long running east and west is a part of a circuit whose resistance is {tex}2.5 \Omega{/tex}. The wire falls to the ground from a height of 5 m. If {tex} g = 10.0 m/s^2 {/tex} and horizontal component of earth's magnetic field is {tex} 2\times 10^{-5} weber/m^2{/tex}, then the current induced in the circuit just before the wire hits the ground will be

A

0.7{tex} \mathrm { A } {/tex}

0.04{tex} \mathrm { A } {/tex}

C

0.02{tex} \mathrm { A } {/tex}

D

0.01{tex} \mathrm { A } {/tex}

##### Explanation

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Q 7. A coil of {tex} 20 \times 20 \mathrm { cm } {/tex} having 30 turns is making 30 rps in a magnetic field of 1 tesla. The peak value of the induced EMF is approximately

A

452{tex} \mathrm { V } {/tex}

226{tex} \mathrm { V } {/tex}

C

113{tex} \mathrm { V } {/tex}

D

339{tex} \mathrm { V } {/tex}

##### Explanation

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Q 8. Two particles each of mass {tex} m {/tex} and charge {tex} q {/tex} are attached to the two ends of a light rigid rod of length {tex} 2 \ell . {/tex} The rod is rotated at a constant angular speed about a perpendicular axis passing through its centre. The ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the centre of the rod is

{tex} \frac { q } { 2 m } {/tex}

B

{tex} \frac { q } { m } {/tex}

C

{tex} \frac { 2 q } { m } {/tex}

D

{tex} \frac { q } { \pi m } {/tex}

##### Explanation

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Q 9. Loop {tex} A {/tex} of radius {tex} r ( r << R ) {/tex} moves towards a constant current carrying loop {tex} B {/tex} with a constant velocity {tex} v {/tex} in such a way that their planes are parallel and coaxial. The distance between the loops when the induced EMF in {tex} \operatorname { loop } A {/tex} is maximum is

A

{tex} R {/tex}

B

{tex} \frac { R } { \sqrt { 2 } } {/tex}

{tex} \frac { R } { 2 } {/tex}

D

{tex} R \left( 1 - \frac { 1 } { \sqrt { 2 } } \right) {/tex}

##### Explanation

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Q 10. A uniform current carrying ring of mass {tex} m {/tex} and radius {tex} R {/tex} is connected by a massless string as shown in Fig. A uniform magnetic field {tex} B _ { 0 } {/tex} exists in the region to keep the ring in horizontal position, then the current in the ring is

{tex} ( \ell = \text { length of string } ) {/tex}

{tex} \frac { m g } { \pi R B _ { 0 } } {/tex}

B

{tex} \frac { m g } { R B _ { 0 } } {/tex}

C

{tex} \frac { m g } { 3 \pi R B _ { 0 } } {/tex}

D

{tex} \frac { m g l } { \pi R ^ { 2 } B _ { 0 } } {/tex}

##### Explanation

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Q 11. A conducting rod {tex} A B {/tex} moves parallel to {tex} x {/tex} -axis in the {tex} x - y {/tex} plane. A uniform magnetic field {tex} B {/tex} pointing normally out of the plane exists throughout the region. A force {tex} F {/tex} acts perpendicular to the rod, so that the rod moves with uniform velocity {tex} v {/tex} . The force {tex} F {/tex} is given by (neglect resistance of all the wires).

{tex} \frac { v B ^ { 2 } l ^ { 2 } } { R } e ^ { - t / R C } {/tex}

B

{tex} \frac { v B ^ { 2 } l ^ { 2 } } { R } {/tex}

C

{tex} \frac { v B ^ { 2 } l ^ { 2 } } { R } \left( 1 - e ^ { - t / R C } \right) {/tex}

D

{tex} \frac { v B ^ { 2 } l ^ { 2 } } { R } \left( 1 - e ^ { - 2 t / R C } \right) {/tex}

##### Explanation

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Q 12. A uniform but time varying magnetic field is present in a circular region of radius {tex} R {/tex} . The magnetic field is perpendicular and into the plane of the paper and the magnitude of the field is increasing at a constant rate {tex} \alpha {/tex} . There is a straight conducing rod of length 2{tex} R {/tex} placed as shown in Fig. The magnitude of induced EMF across the rod is

A

{tex} \pi R ^ { 2 } \alpha {/tex}

B

{tex} \frac { \pi R ^ { 2 } \alpha } { 2 } {/tex}

C

{tex} \frac { R ^ { 2 } \alpha } { \sqrt { 2 } } {/tex}

{tex} \frac { \pi R ^ { 2 } \alpha } { 4 } {/tex}

##### Explanation

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Q 13. The diagram shows a solenoid carrying time varying current {tex} I = I _ { 0 } t . {/tex} On the axis of this solenoid, a ring has been placed. The mutual inductance of the ring and the solenoid is {tex} M {/tex} and the self-inductance of the ring is {tex} L {/tex} . If the resistance of the ring is {tex} R {/tex} then maximum current which can flow through the ring is

A

{tex} \frac { ( 2 M + L ) I _ { 0 } } { R } {/tex}

{tex} \frac { M I _ { 0 } } { R } {/tex}

C

{tex} \frac { ( 2 M - L ) I _ { 0 } } { R } {/tex}

D

{tex} \frac { ( M + L ) I _ { 0 } } { R } {/tex}

##### Explanation

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Q 14. A metallic ring of radius {tex} R {/tex} moves in a vertical plane in the presence of a uniform magnetic field {tex} B {/tex} perpendicular to the plane of the ring. At any given instant of time, its centre of mass moves with a velocity {tex} v {/tex} while ring rotates in its COM frame with angular velocity {tex} \omega {/tex} as shown in Fig. The magnitude of induced EMF between points {tex} O {/tex} and {tex} P {/tex} is

A

Zero

B

{tex} v B R \sqrt { 2 } {/tex}

{tex} v B R {/tex}

D

2{tex} v B R {/tex}

##### Explanation

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Q 15. A very long uniformly charged rod falls with a constant velocity {tex} V {/tex} through the centre of a circular loop. Then the magnitude of induced EMF in loop is

A

{tex} \frac { \mu _ { 0 } } { 2 \pi } \lambda V ^ { 2 } {/tex}

B

{tex} \frac { \mu _ { 0 } } { 2 } \lambda V ^ { 2 } {/tex}

C

{tex} \frac { \mu _ { 0 } } { 2 \lambda } V {/tex}

Zero

##### Explanation

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Q 16. A small square loop of wire of side {tex} \ell {/tex} is placed inside a large square loop of wire of side {tex} L ( L > > \ell ) {/tex} . The loops are coplanar and their centres coincide. The mutual inductance of the system is proportional to

A

{tex} \frac { 1 } { L } {/tex}

{tex} \frac { l ^ { 2 } } { L } {/tex}

C

{tex} \frac { L } { l } {/tex}

D

{tex} \frac { L ^ { 2 } } { l } {/tex}

##### Explanation

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Q 17. In a uniform magnetic field of induction {tex} B , {/tex} a wire in the form of semicircle of radius {tex} r {/tex} rotates about the diameter of the circle with angular frequency {tex} \omega {/tex} . If the total resistance of the circuit is {tex} R , {/tex} the mean power generated per period of rotation is

A

{tex} \frac { B \pi r ^ { 2 } \omega } { 2 R } {/tex}

B

{tex} \frac { \left( B \pi r ^ { 2 } \omega \right) ^ { 2 } } { 2 R } {/tex}

C

{tex} \frac { ( B \pi r \omega ) ^ { 2 } } { 2 R } {/tex}

{tex} \frac { \left( B \pi r ^ { 2 } \omega \right) ^ { 2 } } { 8 R } {/tex}

##### Explanation

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Q 18. A rod of length {tex}\ell{/tex}, negligible resistance, and mass {tex} m {/tex} slides on two horizontal frictionless rails of negligible resistance by hanging a block of mass {tex} m_1{/tex} with the help of insulating a massless string passing through fixed massless pulley (as shown in Fig.). If a constant magnetic field {tex}B{/tex} acts upwards perpendicular to the plan of the figure, the terminal velocity of hanging mass is

A

{tex} \frac { m _ { 1 } g R } { B ^ { 2 } l ^ { 2 } } {/tex} upward

{tex} \frac { m _ { 1 } g R } { B ^ { 2 } l ^ { 2 } } {/tex} downward

C

{tex} \frac { m _ { 1 } g R } { 2 B ^ { 2 } l ^ { 2 } } {/tex} downward

D

{tex} \frac { m _ { 1 } g R } { B ^ { 2 } l } {/tex} downward

##### Explanation

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Q 19. Magnetic field {tex} B _ { 0 } {/tex} exists perpendicular inwards. The resistance of the loop is {tex} R {/tex} . When the switch is closed, the current induced in the circuit is

{tex} \frac { B l v } { R } {/tex}

B

{tex} \frac { 3 B I v } { R } {/tex}

C

{tex} \frac { 2 B I v } { R } {/tex}

D

Zero

##### Explanation

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Q 20. In the circuit shown, each battery has EMF = 5 V. Then the magnetic field at {tex} P {/tex} is

Zero

B

{tex} \frac { 10 \mu _ { 0 } } { R _ { 1 } ( 4 \pi ) ( 0.2 ) } {/tex}

C

{tex} \frac { 20 \mu _ { 0 } } { \left( R _ { 1 } + R _ { 2 } \right) ( 0.8 \pi ) } {/tex}

D

None of these

##### Explanation

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Q 21. The material which shows the effect shown in Fig., when placed in a uniform magnetic field is called

A

Paramagnetic

Diamagnetic

C

Ferromagnetic

D

Anti-ferromagnetic

##### Explanation

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Q 22. A conducting ring of mass {tex}2 \mathrm { kg } {/tex} and radius {tex}0.5 \mathrm { m } {/tex} is placed on a smooth horizontal plane. The ring carries a current {tex} i = 4 \mathrm { A } {/tex} . A horizontal magnetic field {tex} B = 10 \mathrm { T } {/tex} is switched on at time {tex} t = 0 {/tex} as shown in Fig.The initial angular acceleration of the ring will be

40{tex} \pi \ { rad } / \mathrm { s } ^ { 2 } {/tex}

B

20{tex} \pi \ { rad } / \mathrm { s } ^ { 2 } {/tex}

C

5{tex} \pi \ { rad } / \mathrm { s } ^ { 2 } {/tex}

D

15{tex} \pi \ { rad } / \mathrm { s } ^ { 2 } {/tex}

##### Explanation

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Q 23. The EMF induced in a 1 millihenry inductor in which the current changes from 5{tex} \mathrm { A } {/tex} to 3{tex} \mathrm { A } {/tex} in {tex} 10 ^ { - 3 } {/tex} second is

A

{tex} 2 \times 10 ^ { - 6 } \mathrm { V } {/tex}

B

{tex} 8 \times 10 ^ { - 6 } \mathrm { V } {/tex}

2{tex} \mathrm { V } {/tex}

D

8{tex} \mathrm { V } {/tex}

##### Explanation

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Q 24. Conducting circular loop of radius {tex} r {/tex} is placed in {tex} x - y {/tex} plane in gravity free space as shown in Fig., mass of the loop is {tex} m {/tex} and centre of the loop is at the origin. At {tex} t = 0 , {/tex} a current {tex} I {/tex} starts flowing through the loop and a magnetic field {tex} \vec { B } = B _ { 0 } ( \hat { i } + \hat { j } ) {/tex} is switched on in the region (where {tex} B _ { 0 } {/tex} is a constant). The angular acceleration of the loop due to the torque of magnetic field is

A

{tex} \frac { \sqrt { 2 } \pi B _ { 0 } i } { m } {/tex}

{tex} \frac { 2 \sqrt { 2 } \pi B _ { 0 } i } { m } {/tex}

C

{tex} \frac { \pi B _ { 0 } i } { m } {/tex}

D

{tex} \frac { \pi B _ { 0 } i } { 2 m } {/tex}

##### Explanation

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Q 25. A generator produces a voltage that is given by {tex} V = 240 \mathrm { sin } 120 t {/tex}, where {tex} t {/tex} is in seconds. The frequency and {tex} r . m . s {/tex} voltage are

A

{tex} 60 \mathrm { Hz } {/tex} and {tex} 240 \mathrm { V } {/tex}

B

{tex}19 \mathrm { Hz } {/tex} and {tex} 120 \mathrm { V } {/tex}

{tex}19\mathrm { Hz } {/tex} and {tex} 170 \mathrm { V } {/tex}

D

{tex} 754 \mathrm { Hz } {/tex} and {tex} 70 \mathrm { V } {/tex}