Electromagnetic Induction Chapter-Wise Test 15

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A coil is rotated in a magnetic field such that the flux through it changes from maximum to zero. At what position does the rate of change of flux reach its peak?

The rate of change of flux (\( \frac{d\Phi}{dt} = N B A \omega \sin\theta \)) is maximum when \( \sin\theta = 1 \), i.e., at \( \theta = 90^\circ \), where the coil is perpendicular to the field.

Parallel to the field
At 45° to the field
Perpendicular to the field
At 0° to the field
3

A bar magnet is moved towards a coil of 50 turns at a constant speed. The magnetic flux through the coil increases from 0 to 0.02 Wb in 0.1 s. What is the magnitude of the induced emf in the coil?

Given: \( N = 50 \), \( \Delta \Phi_B = 0.02 - 0 = 0.02 \, \text{Wb} \), \( \Delta t = 0.1 \, \text{s} \).

Using Faraday's law: \( \varepsilon = -N \frac{\Delta \Phi_B}{\Delta t} \).

\( \varepsilon = 50 \times \frac{0.02}{0.1} = 50 \times 0.2 = 10 \, \text{V} \).

Magnitude of emf = 10 V.

5 V
8 V
10 V
12 V
3

A circular coil of radius 7 cm and 180 turns rotates at 20 rad/s in a 0.07 T field. What is the maximum emf induced?

\( A = \pi r^2 = 3.14 \times (0.07)^2 = 0.0154 \, \text{m}^2 \).

\( \varepsilon_0 = N B A \omega = 180 \times 0.07 \times 0.0154 \times 20 = 3.88 \, \text{V} \approx 3.9 \, \text{V} \).

3.9 V
4.0 V
4.2 V
4.5 V
1

A square loop of side 15 cm rotates at 15 rad/s in a 0.2 T field. What is the maximum emf induced?

\( A = (0.15)^2 = 0.0225 \, \text{m}^2 \).

\( \varepsilon_0 = N B A \omega = 1 \times 0.2 \times 0.0225 \times 15 = 0.0675 \, \text{V} \).

0.05 V
0.0675 V
0.08 V
0.1 V
2

A coil of 300 turns rotates at 100 rad/s in a 0.05 T field. If the area is 0.01 m², what is the maximum emf?

\( \varepsilon_0 = N B A \omega = 300 \times 0.05 \times 0.01 \times 100 = 15 \, \text{V} \).

10 V
12 V
15 V
18 V
3

A square loop of side 20 cm is rotated in a 0.2 T field at 10 rad/s. What is the maximum emf induced?

\( \varepsilon_0 = N B A \omega \), \( N = 1 \), \( A = (0.2)^2 = 0.04 \, \text{m}^2 \).

\( \varepsilon_0 = 1 \times 0.2 \times 0.04 \times 10 = 0.08 \, \text{V} \).

0.04 V
0.06 V
0.08 V
0.1 V
3

A conducting loop is rotated in a non-uniform magnetic field. The induced emf is more complex than in a uniform field because of what factor?

In a non-uniform field, the magnetic field strength varies across the loop, causing the flux change rate to depend on position, leading to a non-sinusoidal emf.

Constant rotational speed
Loop resistance variation
Uniform flux change
Variation in magnetic field strength
4

A coil of 160 turns and area 0.06 m² is in a field that decreases from 0.08 T to 0 in 0.4 s. What is the induced emf?

\( \Delta \Phi = B A = 0.08 \times 0.06 = 0.0048 \, \text{Wb} \).

\( \varepsilon = N \frac{\Delta \Phi}{\Delta t} = 160 \times \frac{0.0048}{0.4} = 160 \times 0.012 = 1.92 \, \text{V} \).

1.5 V
1.92 V
2.0 V
2.2 V
2

A solenoid of 750 turns/m and area 0.02 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 \( l = 1 \, \text{m} \).

\( L = 1 \times 4\pi \times 10^{-7} \times (750)^2 \times 0.02 \times 1 = 0.01414 \, \text{H} \approx 0.014 \, \text{H} \).

0.01 H
0.012 H
0.014 H
0.016 H
3

A solenoid of 550 turns and length 1.1 m induces an emf of 1.65 V in a nearby coil when its current changes from 0 to 3 A in 0.3 s. What is the mutual inductance?

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

\( \Delta I = 3 - 0 = 3 \, \text{A} \), \( \Delta t = 0.3 \, \text{s} \).

\( M = \frac{\varepsilon}{\frac{\Delta I}{\Delta t}} = \frac{1.65}{\frac{3}{0.3}} = \frac{1.65}{10} = 0.165 \, \text{H} \).

0.165 H
0.18 H
0.2 H
0.22 H
1

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