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  4. Electromagnetic Induction Chapter-Wise Test 2

Electromagnetic Induction Chapter-Wise Test 2

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A solenoid of 700 turns per meter and area 0.015 m² has a current drop from 8 A to 5 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 \( l = 1 \, \text{m} \).

\( L = 4\pi \times 10^{-7} \times (700)^2 \times 0.015 \times 1 = 0.00923 \, \text{H} \).

\( \varepsilon = L \frac{\Delta I}{\Delta t} = 0.00923 \times \frac{5 - 8}{0.3} = 0.00923 \times (-10) = 0.0923 \, \text{V} \approx 0.092 \, \text{V} \).

0.08 V
0.092 V
0.1 V
0.12 V
2

A coil of 300 turns rotates at 70 rad/s in a 0.07 T field. If the area is 0.012 m², what is the maximum emf?

\( \varepsilon_0 = N B A \omega = 300 \times 0.07 \times 0.012 \times 70 = 17.64 \, \text{V} \).

16 V
16.5 V
17 V
17.64 V
4

A loop of 0.2 m × 0.1 m moves out of a 0.5 T field at 2 m/s along its longer side. How long does the emf last?

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

\( t = \frac{0.1}{2} = 0.05 \, \text{s} \).

0.02 s
0.04 s
0.05 s
0.06 s
3

A wheel with 8 spokes of 0.55 m each rotates at 50 rpm in a 0.4 T field. What is the induced emf?

\( \omega = 2\pi \times \frac{50}{60} = \frac{5\pi}{3} \, \text{rad/s} \).

\( \varepsilon = \frac{1}{2} B \omega R^2 = \frac{1}{2} \times 0.4 \times \frac{5\pi}{3} \times (0.55)^2 = 0.3166 \, \text{V} \approx 0.317 \, \text{V} \).

0.25 V
0.28 V
0.3 V
0.317 V
4

A coil of 170 turns and area 0.015 m² is rotated at 35 Hz in a 0.1 T field. What is the maximum emf?

\( \omega = 2\pi v = 2\pi \times 35 = 70\pi \, \text{rad/s} \).

\( \varepsilon_0 = N B A \omega = 170 \times 0.1 \times 0.015 \times 70\pi = 56.03 \, \text{V} \approx 56 \, \text{V} \).

52 V
54 V
55 V
56 V
4

A rod rotates at 15 rad/s in a 0.3 T field. If the length from the axis to the tip is 0.4 m, what is the emf induced?

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

\( \varepsilon = \frac{1}{2} \times 0.3 \times 15 \times (0.4)^2 = 0.36 \, \text{V} \).

0.2 V
0.3 V
0.36 V
0.4 V
3

A coil with high self-inductance is suddenly disconnected from a battery. The resulting high voltage spike is due to what?

The rapid current drop induces a large back emf (\( \varepsilon = -L \frac{dI}{dt} \)) due to self-inductance, causing a voltage spike.

Electrostatic charge buildup
Magnetic field increase
Rapid flux change
Thermal energy release
3

A conducting loop is placed in a uniform magnetic field with its plane parallel to the field lines. Why is no emf induced when the field strength changes?

When the plane is parallel to the field, the flux through the loop is zero (\( \Phi = B A \cos 90^\circ = 0 \)), so changing the field strength does not alter the flux, resulting in no emf.

Due to high resistance
Due to zero flux through the loop
Due to field cancellation
Due to loop motion
2

A solenoid with mutual inductance 0.25 H has a current change of 4 A/s in the primary coil. What is the induced emf in the secondary coil?

\( \varepsilon = M \frac{dI}{dt} = 0.25 \times 4 = 1 \, \text{V} \).

0.5 V
0.75 V
1 V
1.25 V
3

A rectangular loop of 0.1 m × 0.2 m moves out of a 0.4 T field at 0.5 m/s along its shorter side. What is the emf?

\( \varepsilon = B l v \), \( l = 0.2 \, \text{m} \).

\( \varepsilon = 0.4 \times 0.2 \times 0.5 = 0.04 \, \text{V} \).

0.02 V
0.03 V
0.04 V
0.05 V
3

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