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  4. Electromagnetic Induction Chapter-Wise Test 3

Electromagnetic Induction Chapter-Wise Test 3

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A wheel with 5 spokes of 0.4 m each rotates at 30 rpm in a 0.7 T field. What is the induced emf?

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

\( \varepsilon = \frac{1}{2} B \omega R^2 = \frac{1}{2} \times 0.7 \times \pi \times (0.4)^2 = 0.1759 \, \text{V} \approx 0.176 \, \text{V} \).

0.14 V
0.15 V
0.16 V
0.176 V
4

In an AC generator, slip rings are used instead of a split ring commutator. What is the primary reason for this design choice?

Slip rings allow continuous contact with the coil, preserving the alternating nature of the emf, unlike a split ring commutator which rectifies it to DC.

To maintain alternating current output
To increase the generator’s efficiency
To reduce mechanical friction
To convert AC to DC output
1

A coil of 80 turns is placed in a magnetic field that increases from 0 to 0.03 Wb/m² in 0.2 s. If the coil area is 0.05 m², what is the induced emf?

Flux change: \( \Delta \Phi = B A = 0.03 \times 0.05 = 0.0015 \, \text{Wb} \).

\( \varepsilon = N \frac{\Delta \Phi}{\Delta t} = 80 \times \frac{0.0015}{0.2} = 80 \times 0.0075 = 0.6 \, \text{V} \).

0.6 V
0.8 V
1.0 V
1.2 V
1

A circular loop of radius 15 cm is deformed into a straight wire in a 0.15 T field in 0.6 s. What is the induced emf?

Initial flux: \( \Phi = B A = 0.15 \times \pi \times (0.15)^2 = 0.0106 \, \text{Wb} \).

Final flux = 0.

\( \varepsilon = \frac{\Delta \Phi}{\Delta t} = \frac{0.0106}{0.6} = 0.01767 \, \text{V} \approx 0.018 \, \text{V} \).

0.015 V
0.018 V
0.02 V
0.022 V
2

A conducting loop is placed in a magnetic field that remains constant in magnitude and direction. No emf is induced because of what condition?

Emf is induced only when magnetic flux changes. A constant field with a stationary loop results in no flux change, hence no emf.

High loop resistance
No change in magnetic flux
Low field strength
Loop orientation
2

A coil of 130 turns and area 0.04 m² is in a field that increases from 0 to 0.05 T in 0.2 s. What is the induced emf?

\( \Delta \Phi = B A = 0.05 \times 0.04 = 0.002 \, \text{Wb} \).

\( \varepsilon = N \frac{\Delta \Phi}{\Delta t} = 130 \times \frac{0.002}{0.2} = 130 \times 0.01 = 1.3 \, \text{V} \).

1.0 V
1.3 V
1.5 V
1.8 V
2

A solenoid of 550 turns per meter and area 0.016 m² has a current drop from 7 A to 4 A in 0.3 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 \( l = 1 \, \text{m} \).

\( L = 4\pi \times 10^{-7} \times (550)^2 \times 0.016 \times 1 = 0.00608 \, \text{H} \).

\( \varepsilon = L \frac{\Delta I}{\Delta t} = 0.00608 \times \frac{4 - 7}{0.3} = 0.00608 \times (-10) = 0.0608 \, \text{V} \approx 0.061 \, \text{V} \).

0.05 V
0.061 V
0.07 V
0.08 V
2

A solenoid of 700 turns/m and area 0.008 m² has \( \mu_r = 1 \). What is its self-inductance? (\( \mu_0 = 4\pi \times 10^{-7} \, \text{H/m} \))

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

\( L = 1 \times 4\pi \times 10^{-7} \times (700)^2 \times 0.008 \times 1 = 0.00492 \, \text{H} \approx 0.005 \, \text{H} \).

0.003 H
0.004 H
0.005 H
0.006 H
3

A solenoid of 1000 turns/m and area 0.01 m² has \( \mu_r = 2 \). What is its self-inductance? (\( \mu_0 = 4\pi \times 10^{-7} \, \text{H/m} \))

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

\( L = 2 \times 4\pi \times 10^{-7} \times (1000)^2 \times 0.01 \times 1 = 0.02513 \, \text{H} \approx 0.025 \, \text{H} \).

0.02 H
0.022 H
0.025 H
0.03 H
3

A coil of 120 turns and area 0.04 m² is in a 0.09 T field that drops to zero in 0.3 s. What is the induced emf?

\( \Delta \Phi = B A = 0.09 \times 0.04 = 0.0036 \, \text{Wb} \).

\( \varepsilon = N \frac{\Delta \Phi}{\Delta t} = 120 \times \frac{0.0036}{0.3} = 120 \times 0.012 = 1.44 \, \text{V} \).

1.0 V
1.2 V
1.44 V
1.6 V
3

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