Electromagnetic Induction Chapter-Wise Test 13

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A circular coil of radius 4 cm and 250 turns rotates at 40 rad/s in a 0.06 T field. What is the maximum emf induced?

\( A = \pi r^2 = 3.14 \times (0.04)^2 = 0.005024 \, \text{m}^2 \).

\( \varepsilon_0 = N B A \omega = 250 \times 0.06 \times 0.005024 \times 40 = 3.0144 \, \text{V} \approx 3.01 \, \text{V} \).

3.01 V
3.2 V
3.5 V
4.0 V
1

In an AC generator, the maximum emf occurs when the coil is in which orientation relative to the magnetic field?

The maximum emf occurs when the rate of flux change is greatest, which happens when the coil is perpendicular to the field (\( \sin\theta = 1 \)).

Parallel to the field
At 45° to the field
At 60° to the field
Perpendicular to the field
4

A magnet is moved away from a coil, and the induced current flows clockwise as viewed from the magnet. What is the polarity of the coil’s face towards the magnet?

By Lenz’s law, the clockwise current opposes the decreasing flux by producing a south pole facing the receding north pole of the magnet, creating an attractive force.

North
South
Neutral
Alternating
2

A circular coil of radius 5 cm and 100 turns is rotated in a 0.1 T magnetic field at 50 rad/s. What is the maximum emf induced?

Maximum emf: \( \varepsilon_0 = N B A \omega \).

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

\( \varepsilon_0 = 100 \times 0.1 \times 0.00785 \times 50 = 3.925 \, \text{V} \approx 3.93 \, \text{V} \).

2.5 V
3.0 V
3.93 V
4.5 V
3

A rectangular loop of 0.3 m × 0.45 m moves out of a 0.5 T field at 0.9 m/s along its shorter side. What is the emf?

\( \varepsilon = B l v \), \( l = 0.45 \, \text{m} \).

\( \varepsilon = 0.5 \times 0.45 \times 0.9 = 0.2026 \, \text{V} \approx 0.203 \, \text{V} \).

0.18 V
0.19 V
0.2 V
0.203 V
4

A solenoid with mutual inductance 0.22 H has a current change of 7 A/s in the primary coil. What is the induced emf in the secondary coil?

\( \varepsilon = M \frac{dI}{dt} = 0.22 \times 7 = 1.54 \, \text{V} \).

1.2 V
1.4 V
1.54 V
1.6 V
3

A coil with \( L = 0.2 \, \text{H} \) has its current increased from 0 to 5 A in 0.5 s. What is the energy stored?

\( W = \frac{1}{2} L I^2 = \frac{1}{2} \times 0.2 \times (5)^2 = 0.1 \times 25 = 2.5 \, \text{J} \).

2.0 J
2.2 J
2.4 J
2.5 J
4

A circular coil of radius 8 cm and 240 turns rotates at 45 rad/s in a 0.04 T field. What is the maximum emf induced?

\( A = \pi r^2 = 3.14 \times (0.08)^2 = 0.0201 \, \text{m}^2 \).

\( \varepsilon_0 = N B A \omega = 240 \times 0.04 \times 0.0201 \times 45 = 8.676 \, \text{V} \approx 8.68 \, \text{V} \).

8.68 V
9.0 V
9.5 V
10.0 V
1

A coil of 140 turns and area 0.045 m² is in a field that decreases from 0.07 T to 0 in 0.35 s. What is the induced emf?

\( \Delta \Phi = B A = 0.07 \times 0.045 = 0.00315 \, \text{Wb} \).

\( \varepsilon = N \frac{\Delta \Phi}{\Delta t} = 140 \times \frac{0.00315}{0.35} = 140 \times 0.009 = 1.26 \, \text{V} \).

1.0 V
1.26 V
1.5 V
1.8 V
2

A solenoid of 600 turns per meter and area 0.012 m² has a current change from 4 A to 1 A in 0.2 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 \( l = 1 \, \text{m} \).

\( L = 4\pi \times 10^{-7} \times (600)^2 \times 0.012 \times 1 = 0.00543 \, \text{H} \).

\( \varepsilon = L \frac{\Delta I}{\Delta t} = 0.00543 \times \frac{1 - 4}{0.2} = 0.00543 \times (-15) = 0.08145 \, \text{V} \approx 0.081 \, \text{V} \).

0.06 V
0.081 V
0.09 V
0.1 V
2

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