Electromagnetic Induction Chapter-Wise Test 17

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A coil of 100 turns and area 0.02 m² is rotated at 50 Hz in a 0.05 T field. What is the maximum emf?

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

\( \varepsilon_0 = N B A \omega = 100 \times 0.05 \times 0.02 \times 100\pi = 31.4 \, \text{V} \).

25 V
28 V
30 V
31.4 V
4

A solenoid of 450 turns per meter and area 0.018 m² has a current change from 5 A to 2 A in 0.15 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 \( l = 1 \, \text{m} \).

\( L = 4\pi \times 10^{-7} \times (450)^2 \times 0.018 \times 1 = 0.00458 \, \text{H} \).

\( \varepsilon = L \frac{\Delta I}{\Delta t} = 0.00458 \times \frac{2 - 5}{0.15} = 0.00458 \times (-20) = 0.0916 \, \text{V} \approx 0.092 \, \text{V} \).

0.07 V
0.092 V
0.1 V
0.12 V
2

A coil with \( L = 0.4 \, \text{H} \) has its current increased from 0 to 7 A in 0.7 s. What is the energy stored?

\( W = \frac{1}{2} L I^2 = \frac{1}{2} \times 0.4 \times (7)^2 = 0.2 \times 49 = 9.8 \, \text{J} \).

9 J
9.5 J
9.7 J
9.8 J
4

A circular coil of radius 9 cm and 200 turns rotates at 50 rad/s in a 0.03 T field. What is the maximum emf induced?

\( A = \pi r^2 = 3.14 \times (0.09)^2 = 0.0254 \, \text{m}^2 \).

\( \varepsilon_0 = N B A \omega = 200 \times 0.03 \times 0.0254 \times 50 = 7.62 \, \text{V} \).

7.62 V
8.0 V
8.5 V
9.0 V
1

A coil of 150 turns and area 0.05 m² is in a field that increases from 0 to 0.06 T in 0.3 s. What is the induced emf?

\( \Delta \Phi = B A = 0.06 \times 0.05 = 0.003 \, \text{Wb} \).

\( \varepsilon = N \frac{\Delta \Phi}{\Delta t} = 150 \times \frac{0.003}{0.3} = 150 \times 0.01 = 1.5 \, \text{V} \).

1.2 V
1.5 V
1.8 V
2.0 V
2

A coil of 280 turns rotates at 80 rad/s in a 0.06 T field. If the area is 0.01 m², what is the maximum emf?

\( \varepsilon_0 = N B A \omega = 280 \times 0.06 \times 0.01 \times 80 = 13.44 \, \text{V} \).

12 V
12.5 V
13 V
13.44 V
4

A coil is placed near a current-carrying solenoid. The induced emf in the coil is zero when the solenoid’s current is in what state?

A constant current produces a steady magnetic field, resulting in no change in flux through the coil and thus no induced emf.

Increasing linearly
Decreasing rapidly
Steady and unchanging
Oscillating
3

A coil of 130 turns experiences a magnetic flux change from 0 to 0.06 Wb in 0.12 s. What is the induced emf?

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

\( \Delta \Phi = 0.06 \, \text{Wb} \), \( \Delta t = 0.12 \, \text{s} \), \( N = 130 \).

\( \varepsilon = 130 \times \frac{0.06}{0.12} = 130 \times 0.5 = 65 \, \text{V} \).

65 V
70 V
75 V
80 V
1

A conducting loop is rotated in a uniform magnetic field. The induced emf depends on the rate of change of what physical quantity?

Faraday’s law states that the induced emf is proportional to the rate of change of magnetic flux through the loop, which varies as the loop rotates.

Magnetic flux
Magnetic field strength
Loop resistance
Current in the loop
1

A coil of 50 turns and area 0.06 m² is in a 0.15 T field that drops to zero in 0.3 s. What is the induced emf?

\( \Delta \Phi = B A = 0.15 \times 0.06 = 0.009 \, \text{Wb} \).

\( \varepsilon = N \frac{\Delta \Phi}{\Delta t} = 50 \times \frac{0.009}{0.3} = 50 \times 0.03 = 1.5 \, \text{V} \).

1.0 V
1.2 V
1.5 V
1.8 V
3

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