Electromagnetic Induction Chapter-Wise Test 14

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A rod of length 0.8 m moves at 1.5 m/s in a 0.4 T field perpendicular to its length. What is the induced emf?

\( \varepsilon = B l v = 0.4 \times 0.8 \times 1.5 = 0.48 \, \text{V} \).

0.48 V
0.5 V
0.55 V
0.6 V
1

A wheel with 4 spokes of 0.5 m each rotates at 48 rpm in a 0.8 T field. What is the induced emf?

\( \omega = 2\pi \times \frac{48}{60} = 1.6\pi \, \text{rad/s} \).

\( \varepsilon = \frac{1}{2} B \omega R^2 = \frac{1}{2} \times 0.8 \times 1.6\pi \times (0.5)^2 = 0.5024 \, \text{V} \approx 0.5 \, \text{V} \).

0.4 V
0.45 V
0.48 V
0.5 V
4

A rectangular loop of sides 15 cm and 6 cm moves out of a 0.4 T field at 1.5 m/s perpendicular to the shorter side. What is the motional emf?

\( \varepsilon = B l v \), \( l = 0.15 \, \text{m} \).

\( \varepsilon = 0.4 \times 0.15 \times 1.5 = 0.09 \, \text{V} \).

0.09 V
0.12 V
0.15 V
0.18 V
1

A solenoid of 800 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 \( l = 1 \, \text{m} \).

\( L = 1 \times 4\pi \times 10^{-7} \times (800)^2 \times 0.01 \times 1 = 0.00804 \, \text{H} \approx 0.008 \, \text{H} \).

0.005 H
0.006 H
0.008 H
0.01 H
3

A solenoid with mutual inductance 0.3 H has a current change of 5 A/s in the primary coil. What is the induced emf in the secondary coil?

\( \varepsilon = M \frac{dI}{dt} = 0.3 \times 5 = 1.5 \, \text{V} \).

1.0 V
1.2 V
1.5 V
1.8 V
3

A rod rotates at 20 rad/s in a 0.4 T field. If the length from the axis to the tip is 0.5 m, what is the emf induced?

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

\( \varepsilon = \frac{1}{2} \times 0.4 \times 20 \times (0.5)^2 = 5 \, \text{V} \).

2.5 V
4 V
5 V
6 V
3

When a bar magnet is moved towards a stationary coil, the induced current flows in a direction that opposes the magnet’s motion. This is an example of which fundamental principle?

The phenomenon where induced current opposes the change causing it is Lenz’s law, which ensures conservation of energy by resisting the magnet’s motion through a repulsive force.

Lenz’s law
Faraday’s law
Ampere’s law
Gauss’s law
1

A conducting rod is moved perpendicular to a uniform magnetic field. The emf induced across its ends depends on which of the following factors?

The motional emf is given by \( \varepsilon = B l v \), where \( B \) is the magnetic field strength, \( l \) is the length of the rod, and \( v \) is its velocity, all of which are critical factors.

Magnetic field strength, length of the rod, and velocity
Only magnetic field strength
Only velocity of the rod
Mass of the rod and magnetic field
1

A metal ring is placed near a solenoid. When an AC current flows through the solenoid, the ring experiences a force. This is primarily due to what?

The AC current creates a varying magnetic field, inducing currents in the ring that generate an opposing field, leading to a repulsive or attractive force based on Lenz’s law.

Electrostatic attraction
Gravitational interaction
Interaction of induced currents with the magnetic field
Thermal expansion
3

A rectangular loop of sides 30 cm and 12 cm moves out of a 0.6 T field at 1 m/s perpendicular to the shorter side. What is the motional emf?

\( \varepsilon = B l v \), \( l = 0.3 \, \text{m} \).

\( \varepsilon = 0.6 \times 0.3 \times 1 = 0.18 \, \text{V} \).

0.18 V
0.2 V
0.22 V
0.25 V
1

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