Electromagnetic Induction Chapter-Wise Test 12

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A rectangular loop of 0.24 m × 0.38 m moves out of a 0.3 T field at 0.6 m/s along its shorter side. What is the emf?

\( \varepsilon = B l v \), \( l = 0.38 \, \text{m} \).

\( \varepsilon = 0.3 \times 0.38 \times 0.6 = 0.0684 \, \text{V} \approx 0.068 \, \text{V} \).

0.05 V
0.06 V
0.065 V
0.068 V
4

A coil of self-inductance 0.4 H has its current decreased from 5 A to 2 A in 0.1 s. What is the magnitude of the induced emf?

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

\( \Delta I = 2 - 5 = -3 \, \text{A} \), \( \Delta t = 0.1 \, \text{s} \).

\( \varepsilon = 0.4 \times \frac{-3}{0.1} = 0.4 \times (-30) = -12 \, \text{V} \).

Magnitude = 12 V.

8 V
10 V
12 V
15 V
3

A wheel with 10 spokes of 0.7 m each rotates at 60 rpm in a 0.5 T field. What is the induced emf?

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

\( \varepsilon = \frac{1}{2} B \omega R^2 = \frac{1}{2} \times 0.5 \times 2\pi \times (0.7)^2 = 0.7697 \, \text{V} \approx 0.77 \, \text{V} \).

0.6 V
0.7 V
0.75 V
0.77 V
4

A conducting loop is shrunk in a uniform magnetic field. The induced current flows in a direction to oppose what change?

Shrinking the loop decreases the magnetic flux through it. Lenz’s law states the induced current opposes this decrease by creating a field in the same direction as the original field.

Increase in magnetic field
Increase in loop area
Decrease in magnetic flux
Decrease in loop resistance
3

A square loop of side 26 cm rotates at 12 rad/s in a 0.3 T field. What is the maximum emf induced?

\( A = (0.26)^2 = 0.0676 \, \text{m}^2 \).

\( \varepsilon_0 = N B A \omega = 1 \times 0.3 \times 0.0676 \times 12 = 0.24336 \, \text{V} \approx 0.243 \, \text{V} \).

0.2 V
0.243 V
0.28 V
0.3 V
2

A solenoid with mutual inductance 0.25 H has a current change of 6 A/s in the primary coil. What is the induced emf in the secondary coil?

\( \varepsilon = M \frac{dI}{dt} = 0.25 \times 6 = 1.5 \, \text{V} \).

1.0 V
1.2 V
1.5 V
1.8 V
3

A rectangular loop of 0.36 m × 0.5 m moves out of a 0.55 T field at 0.8 m/s along its shorter side. What is the emf?

\( \varepsilon = B l v \), \( l = 0.5 \, \text{m} \).

\( \varepsilon = 0.55 \times 0.5 \times 0.8 = 0.22 \, \text{V} \).

0.18 V
0.2 V
0.21 V
0.22 V
4

A solenoid’s current is increased, and the energy stored in its magnetic field increases. This energy is analogous to what mechanical quantity?

The energy (\( \frac{1}{2} L I^2 \)) is analogous to kinetic energy (\( \frac{1}{2} m v^2 \)), with inductance acting like mass and current like velocity.

Potential energy
Momentum
Work
Kinetic energy
4

A loop of 0.35 m × 0.1 m moves out of a 0.25 T field at 2.5 m/s along its longer side. How long does the emf last?

Time = distance/velocity, distance = width along motion = 0.1 m.

\( t = \frac{0.1}{2.5} = 0.04 \, \text{s} \).

0.02 s
0.03 s
0.04 s
0.05 s
3

A loop of 0.32 m × 0.16 m moves out of a 0.35 T field at 2 m/s along its longer side. How long does the emf last?

Time = distance/velocity, distance = width along motion = 0.16 m.

\( t = \frac{0.16}{2} = 0.08 \, \text{s} \).

0.06 s
0.07 s
0.08 s
0.09 s
3

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