Electromagnetic Induction Chapter-Wise Test 2

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A coil is placed in a uniform magnetic field of 0.5 T. The area of the coil is 0.04 m², and the angle between the field and the area vector changes from 0° to 90° in 0.2 s. What is the induced emf?

Initial flux: \( \Phi_i = B A \cos 0^\circ = 0.5 \times 0.04 \times 1 = 0.02 \, \text{Wb} \).

Final flux: \( \Phi_f = B A \cos 90^\circ = 0.5 \times 0.04 \times 0 = 0 \, \text{Wb} \).

\( \Delta \Phi = 0.02 - 0 = 0.02 \, \text{Wb} \), \( \Delta t = 0.2 \, \text{s} \).

\( \varepsilon = -\frac{\Delta \Phi}{\Delta t} = \frac{0.02}{0.2} = 0.1 \, \text{V} \).

0.05 V
0.1 V
0.2 V
0.25 V
2

A coil of 200 turns and area 0.04 m² is rotated at 50 Hz in a 0.1 T field. What is the maximum emf?

\( \omega = 2\pi v = 2\pi \times 50 = 100\pi \, \text{rad/s} \).

\( \varepsilon_0 = N B A \omega = 200 \times 0.1 \times 0.04 \times 100\pi = 251.33 \, \text{V} \approx 251.3 \, \text{V} \).

248 V
250 V
251 V
251.3 V
4

A coil of 110 turns and area 0.035 m² is in a field that decreases from 0.09 T to 0 in 0.5 s. What is the induced emf?

\( \Delta \Phi = B A = 0.09 \times 0.035 = 0.00315 \, \text{Wb} \).

\( \varepsilon = N \frac{\Delta \Phi}{\Delta t} = 110 \times \frac{0.00315}{0.5} = 110 \times 0.0063 = 0.693 \, \text{V} \approx 0.69 \, \text{V} \).

0.5 V
0.69 V
0.8 V
0.9 V
2

A coil of 180 turns rotates at 60 rad/s in a 0.03 T field. If the area is 0.02 m², what is the maximum emf?

\( \varepsilon_0 = N B A \omega = 180 \times 0.03 \times 0.02 \times 60 = 6.48 \, \text{V} \).

5.5 V
6.0 V
6.2 V
6.48 V
4

A loop of 0.28 m × 0.14 m moves out of a 0.3 T field at 1.4 m/s along its longer side. How long does the emf last?

Time = distance/velocity, distance = width along motion = 0.14 m.

\( t = \frac{0.14}{1.4} = 0.1 \, \text{s} \).

0.08 s
0.09 s
0.1 s
0.12 s
3

A rod rotates at 25 rad/s in a 0.5 T field. If the length from the axis to the tip is 0.7 m, what is the emf induced?

\( \varepsilon = \frac{1}{2} B \omega R^2 \).

\( \varepsilon = \frac{1}{2} \times 0.5 \times 25 \times (0.7)^2 = 3.0625 \, \text{V} \approx 3.06 \, \text{V} \).

2.8 V
3.0 V
3.06 V
3.2 V
3

A rod rotates at 12 rad/s in a 0.5 T field. If the length from the axis to the tip is 0.9 m, what is the emf induced?

\( \varepsilon = \frac{1}{2} B \omega R^2 \).

\( \varepsilon = \frac{1}{2} \times 0.5 \times 12 \times (0.9)^2 = 2.43 \, \text{V} \).

2.0 V
2.2 V
2.43 V
2.6 V
3

A solenoid with mutual inductance 0.4 H has a current change of 3 A/s in the primary coil. What is the induced emf in the secondary coil?

\( \varepsilon = M \frac{dI}{dt} = 0.4 \times 3 = 1.2 \, \text{V} \).

0.8 V
1.0 V
1.2 V
1.4 V
3

A rod of length 0.4 m moves at 2 m/s in a 0.3 T field perpendicular to its length. What is the induced emf?

\( \varepsilon = B l v = 0.3 \times 0.4 \times 2 = 0.24 \, \text{V} \).

0.24 V
0.28 V
0.3 V
0.35 V
1

A solenoid of 650 turns and length 1.2 m induces an emf of 2.6 V in a nearby coil when its current changes from 2 A to 6 A in 0.4 s. What is the mutual inductance?

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

\( \Delta I = 6 - 2 = 4 \, \text{A} \), \( \Delta t = 0.4 \, \text{s} \).

\( M = \frac{\varepsilon}{\frac{\Delta I}{\Delta t}} = \frac{2.6}{\frac{4}{0.4}} = \frac{2.6}{10} = 0.26 \, \text{H} \).

0.26 H
0.28 H
0.3 H
0.32 H
1

Performance Summary

Score:

Category Details
Total Attempts:
Total Skipped:
Total Wrong Answers:
Total Correct Answers:
Time Taken:
Average Time Taken per Question:
Accuracy:
0