Electromagnetic Induction Chapter-Wise Test 4

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A rectangular loop of 0.15 m × 0.25 m moves out of a 0.3 T field at 0.8 m/s along its shorter side. What is the emf?

\( \varepsilon = B l v \), \( l = 0.25 \, \text{m} \).

\( \varepsilon = 0.3 \times 0.25 \times 0.8 = 0.06 \, \text{V} \).

0.04 V
0.05 V
0.055 V
0.06 V
4

A wheel with 8 spokes of 0.25 m each rotates at 60 rpm in a 0.5 T field. What is the induced emf?

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

\( \varepsilon = \frac{1}{2} B \omega R^2 = \frac{1}{2} \times 0.5 \times 2\pi \times (0.25)^2 = 0.098 \, \text{V} \approx 0.1 \, \text{V} \).

0.05 V
0.1 V
0.15 V
0.2 V
2

A circular coil of radius 5 cm and 300 turns rotates at 35 rad/s in a 0.05 T field. What is the maximum emf induced?

\( A = \pi r^2 = 3.14 \times (0.05)^2 = 0.00785 \, \text{m}^2 \).

\( \varepsilon_0 = N B A \omega = 300 \times 0.05 \times 0.00785 \times 35 = 4.12375 \, \text{V} \approx 4.12 \, \text{V} \).

4.12 V
4.5 V
4.8 V
5.0 V
1

A loop enters a magnetic field region with its plane perpendicular to the field. The induced current flows to produce a magnetic field opposing what?

The current opposes the increase in flux as the loop enters the field, creating a field opposite to the external field per Lenz’s law.

Decrease in flux
Decrease in loop area
Increase in flux
Increase in resistance
3

In an AC generator, the emf varies sinusoidally with time. What is the primary reason for this variation?

The emf varies sinusoidally because the coil rotates in a uniform magnetic field, causing the angle between the magnetic field and the coil’s area vector to change continuously, following a sine function.

Rotation of the coil in a uniform magnetic field
Change in the magnetic field strength
Variation in the coil’s resistance
Presence of a variable capacitor
1

A conducting rod slides along parallel rails in a magnetic field perpendicular to its motion. The emf induced in the circuit is classified as what type?

This is motional emf, as it arises from the rod’s motion through the magnetic field, cutting flux lines to induce a potential difference.

Motional emf
Static emf
Thermal emf
Chemical emf
1

A solenoid of 850 turns/m and area 0.01 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 \( l = 1 \, \text{m} \).

\( L = 1 \times 4\pi \times 10^{-7} \times (850)^2 \times 0.01 \times 1 = 0.00907 \, \text{H} \approx 0.009 \, \text{H} \).

0.007 H
0.008 H
0.009 H
0.01 H
3

A coil of 90 turns experiences a magnetic flux change from 0 to 0.025 Wb in 0.05 s. What is the induced emf?

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

\( \Delta \Phi = 0.025 \, \text{Wb} \), \( \Delta t = 0.05 \, \text{s} \), \( N = 90 \).

\( \varepsilon = 90 \times \frac{0.025}{0.05} = 90 \times 0.5 = 45 \, \text{V} \).

45 V
50 V
55 V
60 V
1

A solenoid of 950 turns/m and area 0.012 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 \( l = 1 \, \text{m} \).

\( L = 1 \times 4\pi \times 10^{-7} \times (950)^2 \times 0.012 \times 1 = 0.0136 \, \text{H} \approx 0.014 \, \text{H} \).

0.01 H
0.012 H
0.014 H
0.016 H
3

A conducting loop is moved out of a magnetic field region. The induced current flows to oppose what specific change?

Moving the loop out reduces the magnetic flux through it, and the induced current opposes this decrease by generating a field in the same direction as the original field.

Increase in field strength
Increase in loop area
Decrease in magnetic flux
Increase in loop resistance
3

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