Electromagnetic Induction Chapter-Wise Test 22

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A coil of 230 turns rotates at 85 rad/s in a 0.03 T field. If the area is 0.02 m², what is the maximum emf?

\( \varepsilon_0 = N B A \omega = 230 \times 0.03 \times 0.02 \times 85 = 11.73 \, \text{V} \).

10 V
11 V
11.5 V
11.73 V
4

A coil of 170 turns and area 0.07 m² is in a field that decreases from 0.1 T to 0 in 0.5 s. What is the induced emf?

\( \Delta \Phi = B A = 0.1 \times 0.07 = 0.007 \, \text{Wb} \).

\( \varepsilon = N \frac{\Delta \Phi}{\Delta t} = 170 \times \frac{0.007}{0.5} = 170 \times 0.014 = 2.38 \, \text{V} \).

2.0 V
2.38 V
2.5 V
2.8 V
2

A wheel with 7 spokes of 0.45 m each rotates at 36 rpm in a 0.6 T field. What is the induced emf?

\( \omega = 2\pi \times \frac{36}{60} = 1.2\pi \, \text{rad/s} \).

\( \varepsilon = \frac{1}{2} B \omega R^2 = \frac{1}{2} \times 0.6 \times 1.2\pi \times (0.45)^2 = 0.383 \, \text{V} \approx 0.38 \, \text{V} \).

0.3 V
0.35 V
0.37 V
0.38 V
4

A square loop of side 20 cm rotates at 20 rad/s in a 0.15 T field. What is the maximum emf induced?

\( A = (0.2)^2 = 0.04 \, \text{m}^2 \).

\( \varepsilon_0 = N B A \omega = 1 \times 0.15 \times 0.04 \times 20 = 0.12 \, \text{V} \).

0.1 V
0.12 V
0.14 V
0.16 V
2

A circular loop of radius 12 cm is deformed into a straight wire in a 0.2 T field in 0.5 s. What is the induced emf?

Initial flux: \( \Phi = B A = 0.2 \times \pi \times (0.12)^2 = 0.00904 \, \text{Wb} \).

Final flux = 0.

\( \varepsilon = \frac{\Delta \Phi}{\Delta t} = \frac{0.00904}{0.5} = 0.01808 \, \text{V} \approx 0.018 \, \text{V} \).

0.01 V
0.018 V
0.02 V
0.025 V
2

A coil of 70 turns experiences a magnetic flux change from 0 to 0.02 Wb in 0.04 s. What is the induced emf?

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

\( \Delta \Phi = 0.02 \, \text{Wb} \), \( \Delta t = 0.04 \, \text{s} \), \( N = 70 \).

\( \varepsilon = 70 \times \frac{0.02}{0.04} = 70 \times 0.5 = 35 \, \text{V} \).

35 V
40 V
45 V
50 V
1

A solenoid of 500 turns per meter and area 0.01 m² has a current change from 3 A to 0 A in 0.5 s. What is the self-induced emf? (\( \mu_0 = 4\pi \times 10^{-7} \, \text{H/m} \))

\( L = \mu_0 n^2 A l \), assume \( l = 1 \, \text{m} \).

\( L = 4\pi \times 10^{-7} \times (500)^2 \times 0.01 \times 1 = 0.00314 \, \text{H} \).

\( \varepsilon = L \frac{\Delta I}{\Delta t} = 0.00314 \times \frac{0 - 3}{0.5} = 0.01884 \, \text{V} \approx 0.019 \, \text{V} \).

0.015 V
0.019 V
0.022 V
0.025 V
2

A solenoid’s current is switched off suddenly. What causes sensitive instruments nearby to be at risk of damage?

The sudden drop in current induces a high emf due to self-inductance, which can generate significant currents or voltages in nearby circuits, risking damage.

Electrostatic discharge
Magnetic field saturation
High induced emf
Thermal expansion
3

A coil of self-inductance 1.0 H has its current decreased from 5 A to 2 A in 0.15 s. What is the magnitude of the induced emf?

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

\( \Delta I = 2 - 5 = -3 \, \text{A} \), \( \Delta t = 0.15 \, \text{s} \).

\( \varepsilon = 1.0 \times \frac{-3}{0.15} = 1.0 \times (-20) = -20 \, \text{V} \), magnitude = 20 V.

15 V
20 V
25 V
30 V
2

A coil of 130 turns and area 0.03 m² is rotated at 30 Hz in a 0.08 T field. What is the maximum emf?

\( \omega = 2\pi v = 2\pi \times 30 = 60\pi \, \text{rad/s} \).

\( \varepsilon_0 = N B A \omega = 130 \times 0.08 \times 0.03 \times 60\pi = 58.62 \, \text{V} \).

55 V
56 V
57 V
58.62 V
4

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