Electromagnetic Induction Chapter-Wise Test 20

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A circular loop of radius 14 cm is deformed into a straight wire in a 0.15 T field in 0.5 s. What is the induced emf?

Initial flux: \( \Phi = B A = 0.15 \times \pi \times (0.14)^2 = 0.00923 \, \text{Wb} \).

Final flux = 0.

\( \varepsilon = \frac{\Delta \Phi}{\Delta t} = \frac{0.00923}{0.5} = 0.01846 \, \text{V} \approx 0.018 \, \text{V} \).

0.015 V
0.018 V
0.02 V
0.025 V
2

A coil of 320 turns rotates at 65 rad/s in a 0.08 T field. If the area is 0.015 m², what is the maximum emf?

\( \varepsilon_0 = N B A \omega = 320 \times 0.08 \times 0.015 \times 65 = 24.96 \, \text{V} \).

23 V
24 V
24.5 V
24.96 V
4

A coil of 260 turns rotates at 75 rad/s in a 0.05 T field. If the area is 0.018 m², what is the maximum emf?

\( \varepsilon_0 = N B A \omega = 260 \times 0.05 \times 0.018 \times 75 = 17.55 \, \text{V} \).

16 V
16.5 V
17 V
17.55 V
4

A conducting disc rotates in a uniform magnetic field parallel to its axis. The induced emf between the center and rim arises due to what?

Rotation causes radial charge separation via the magnetic force (\( F = q v \times B \)), inducing an emf from the center to the rim.

Change in field direction
Electrostatic induction
Magnetic force on charges
Thermal expansion
3

A wheel with 9 spokes of 0.5 m each rotates at 55 rpm in a 0.6 T field. What is the induced emf?

\( \omega = 2\pi \times \frac{55}{60} = \frac{11\pi}{6} \, \text{rad/s} \).

\( \varepsilon = \frac{1}{2} B \omega R^2 = \frac{1}{2} \times 0.6 \times \frac{11\pi}{6} \times (0.5)^2 = 0.4328 \, \text{V} \approx 0.43 \, \text{V} \).

0.35 V
0.4 V
0.42 V
0.43 V
4

A coil of 40 turns experiences a magnetic flux change from 0 to 0.01 Wb in 0.05 s. What is the induced emf?

\( \varepsilon = N \frac{\Delta \Phi}{\Delta t} \).

\( \Delta \Phi = 0.01 \, \text{Wb} \), \( \Delta t = 0.05 \, \text{s} \), \( N = 40 \).

\( \varepsilon = 40 \times \frac{0.01}{0.05} = 40 \times 0.2 = 8 \, \text{V} \).

8 V
10 V
12 V
14 V
1

A coil of self-inductance 0.5 H has its current increased from 1 A to 4 A in 0.25 s. What is the magnitude of the induced emf?

\( \varepsilon = L \frac{\Delta I}{\Delta t} \).

\( \Delta I = 4 - 1 = 3 \, \text{A} \), \( \Delta t = 0.25 \, \text{s} \).

\( \varepsilon = 0.5 \times \frac{3}{0.25} = 0.5 \times 12 = 6 \, \text{V} \).

4 V
6 V
8 V
10 V
2

A conducting rod is stationary in a varying magnetic field. The induced emf in the rod arises due to which component of the force on its charges?

For a stationary rod (\( v = 0 \)), the emf is induced by the electric field generated by the time-varying magnetic field, not the magnetic force (\( q v \times B \)), which requires motion.

Magnetic force only
Electric field due to changing magnetic field
Gravitational force
Frictional force
2

A coil with \( L = 0.1 \, \text{H} \) has its current increased from 0 to 4 A in 0.2 s. What is the energy stored?

Energy: \( W = \frac{1}{2} L I^2 \).

\( W = \frac{1}{2} \times 0.1 \times (4)^2 = 0.05 \times 16 = 0.8 \, \text{J} \).

0.4 J
0.6 J
0.8 J
1.0 J
3

A solenoid of 350 turns and length 0.7 m induces an emf of 1.2 V in a nearby coil when its current changes from 1 A to 4 A in 0.3 s. What is the mutual inductance?

\( \varepsilon = M \frac{\Delta I}{\Delta t} \).

\( \Delta I = 4 - 1 = 3 \, \text{A} \), \( \Delta t = 0.3 \, \text{s} \).

\( M = \frac{\varepsilon}{\frac{\Delta I}{\Delta t}} = \frac{1.2}{\frac{3}{0.3}} = \frac{1.2}{10} = 0.12 \, \text{H} \).

0.12 H
0.15 H
0.18 H
0.2 H
1

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