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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
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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
0.66{tex} \mathrm { Wbs } ^ { - 2 } {/tex}
1.5{tex} \mathrm { Wbs } ^ { - 2 } {/tex}
{tex} - 0.66 \mathrm { Wbs } ^ { - 2 } {/tex}
{tex} - 1.5 \mathrm { Wbs } ^ { - 2 } {/tex}
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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
{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}
{tex} \pi r ^ { 2 } \left( \frac { d B } { d t } \right) {/tex}
{tex} B \frac { \pi r ^ { 2 } } { 2 } \frac { d r } { d t } {/tex}
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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
{tex} \frac { \left( \phi _ { 2 } - \phi _ { 1 } \right) } { R } {/tex}
{tex} \frac { n \left( \phi _ { 2 } - \phi _ { 1 } \right) } { R } {/tex}
{tex} \frac { \left( \phi _ { 2 } - \phi _ { 1 } \right) } { n R } {/tex}
{tex} \frac { n R } { \left( \phi _ { 2 } - \phi _ { 1 } \right) } {/tex}
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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
3{tex} \mathrm { V } {/tex}
9{tex} \mathrm { V } {/tex}
18{tex} \mathrm { V } {/tex}
27{tex} \mathrm { V } {/tex}
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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
0.7{tex} \mathrm { A } {/tex}
0.04{tex} \mathrm { A } {/tex}
0.02{tex} \mathrm { A } {/tex}
0.01{tex} \mathrm { A } {/tex}
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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
452{tex} \mathrm { V } {/tex}
226{tex} \mathrm { V } {/tex}
113{tex} \mathrm { V } {/tex}
339{tex} \mathrm { V } {/tex}
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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}
{tex} \frac { q } { m } {/tex}
{tex} \frac { 2 q } { m } {/tex}
{tex} \frac { q } { \pi m } {/tex}
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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
{tex} R {/tex}
{tex} \frac { R } { \sqrt { 2 } } {/tex}
{tex} \frac { R } { 2 } {/tex}
{tex} R \left( 1 - \frac { 1 } { \sqrt { 2 } } \right) {/tex}
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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}
{tex} \frac { m g } { R B _ { 0 } } {/tex}
{tex} \frac { m g } { 3 \pi R B _ { 0 } } {/tex}
{tex} \frac { m g l } { \pi R ^ { 2 } B _ { 0 } } {/tex}
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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}
{tex} \frac { v B ^ { 2 } l ^ { 2 } } { R } {/tex}
{tex} \frac { v B ^ { 2 } l ^ { 2 } } { R } \left( 1 - e ^ { - t / R C } \right) {/tex}
{tex} \frac { v B ^ { 2 } l ^ { 2 } } { R } \left( 1 - e ^ { - 2 t / R C } \right) {/tex}
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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
{tex} \pi R ^ { 2 } \alpha {/tex}
{tex} \frac { \pi R ^ { 2 } \alpha } { 2 } {/tex}
{tex} \frac { R ^ { 2 } \alpha } { \sqrt { 2 } } {/tex}
{tex} \frac { \pi R ^ { 2 } \alpha } { 4 } {/tex}
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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
{tex} \frac { ( 2 M + L ) I _ { 0 } } { R } {/tex}
{tex} \frac { M I _ { 0 } } { R } {/tex}
{tex} \frac { ( 2 M - L ) I _ { 0 } } { R } {/tex}
{tex} \frac { ( M + L ) I _ { 0 } } { R } {/tex}
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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
Zero
{tex} v B R \sqrt { 2 } {/tex}
{tex} v B R {/tex}
2{tex} v B R {/tex}
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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
{tex} \frac { \mu _ { 0 } } { 2 \pi } \lambda V ^ { 2 } {/tex}
{tex} \frac { \mu _ { 0 } } { 2 } \lambda V ^ { 2 } {/tex}
{tex} \frac { \mu _ { 0 } } { 2 \lambda } V {/tex}
Zero
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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
{tex} \frac { 1 } { L } {/tex}
{tex} \frac { l ^ { 2 } } { L } {/tex}
{tex} \frac { L } { l } {/tex}
{tex} \frac { L ^ { 2 } } { l } {/tex}
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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
{tex} \frac { B \pi r ^ { 2 } \omega } { 2 R } {/tex}
{tex} \frac { \left( B \pi r ^ { 2 } \omega \right) ^ { 2 } } { 2 R } {/tex}
{tex} \frac { ( B \pi r \omega ) ^ { 2 } } { 2 R } {/tex}
{tex} \frac { \left( B \pi r ^ { 2 } \omega \right) ^ { 2 } } { 8 R } {/tex}
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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
{tex} \frac { m _ { 1 } g R } { B ^ { 2 } l ^ { 2 } } {/tex} upward
{tex} \frac { m _ { 1 } g R } { B ^ { 2 } l ^ { 2 } } {/tex} downward
{tex} \frac { m _ { 1 } g R } { 2 B ^ { 2 } l ^ { 2 } } {/tex} downward
{tex} \frac { m _ { 1 } g R } { B ^ { 2 } l } {/tex} downward
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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}
{tex} \frac { 3 B I v } { R } {/tex}
{tex} \frac { 2 B I v } { R } {/tex}
Zero
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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
{tex} \frac { 10 \mu _ { 0 } } { R _ { 1 } ( 4 \pi ) ( 0.2 ) } {/tex}
{tex} \frac { 20 \mu _ { 0 } } { \left( R _ { 1 } + R _ { 2 } \right) ( 0.8 \pi ) } {/tex}
None of these
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Q 21. The material which shows the effect shown in Fig., when placed in a uniform magnetic field is called
Paramagnetic
Diamagnetic
Ferromagnetic
Anti-ferromagnetic
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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}
20{tex} \pi \ { rad } / \mathrm { s } ^ { 2 } {/tex}
5{tex} \pi \ { rad } / \mathrm { s } ^ { 2 } {/tex}
15{tex} \pi \ { rad } / \mathrm { s } ^ { 2 } {/tex}
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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
{tex} 2 \times 10 ^ { - 6 } \mathrm { V } {/tex}
{tex} 8 \times 10 ^ { - 6 } \mathrm { V } {/tex}
2{tex} \mathrm { V } {/tex}
8{tex} \mathrm { V } {/tex}
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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
{tex} \frac { \sqrt { 2 } \pi B _ { 0 } i } { m } {/tex}
{tex} \frac { 2 \sqrt { 2 } \pi B _ { 0 } i } { m } {/tex}
{tex} \frac { \pi B _ { 0 } i } { m } {/tex}
{tex} \frac { \pi B _ { 0 } i } { 2 m } {/tex}
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Q 25. In an oscillating {tex} L C {/tex} circuit the maximum charge on the capacitor is {tex} Q {/tex}. The charge on the capacitor when the energy is stored equally between the electric and magnetic field is
{tex} Q / 2 {/tex}
{tex} Q / \sqrt { 3 } {/tex}
{tex} Q / \sqrt { 2 } {/tex}
{tex} Q {/tex}
