JEE Physics Electromagnetic Induction MCQs Set 17

Answer: (c) 2 s

Explanation:
1. \( e = -L \) di/dt and di/dt = \( (2t - t^{2}) e^{-t} \).
2. This is zero when \( 2t = t^{2} \), i.e. \( t = 2 s \).

Teacher's Note:
1. Recall the basic law.

Answer: (b) henry (H)

Explanation:
1. \( L \) = emf × \( t/I \) and [emf] = ML²T⁻²Q⁻¹, \( [I] \) = QT⁻¹, so \( [L] \) = ML²Q⁻². This is the dimension of henry.

Teacher's Note:
1. Recall the basic law.

Answer: (a) \( 2.05\times10^{-3}\ \text{W} \)

Explanation:
1. \( e_0 \) = NBAω = \( 20 \times 0.02 \times \pi(0.06)^{2} \times 40 = 0.181 V \).
2. Mean power = \( e_0^{2}/(2R) = 0.0327/16 = 2.05 \times 10^{-3} W \).

Teacher's Note:
1. Recall the basic law.

Answer: (a) self induction

Explanation:
1. By definition this is self induction.

Teacher's Note:
1. Recall the basic law.

Answer: (d) square, reduced

Explanation:
1. Heat produced is proportional to \( i^{2}R \), i.e. the square of the current.
2. Reducing the eddy currents therefore reduces the loss substantially.

Teacher's Note:
1. Recall the basic law.

Answer: (b) a neighbouring coil

Explanation:
1. Mutual induction involves a change of current in a neighbouring coil.

Teacher's Note:
1. Recall the basic law.

Answer: (c) the total number of magnetic field lines passing normally through a given area

Explanation:
1. Flux = \( B A \cos(\theta) \), i.e. the number of field lines crossing the area.

Teacher's Note:
1. Recall the basic law.

Answer: (c) A is true, but R is false.

Explanation:
1. An emf is induced whenever the flux changes.
2. A current flows only if the circuit is closed, so the reason is false.

Teacher's Note:
1. Emf always, current only in a closed circuit.

Answer: (d) anticlockwise

Explanation:
1. The induced eddy currents must produce a north pole facing the magnet to repel it.
2. A north-pole face carries anticlockwise current when viewed from that side.

Teacher's Note:
1. Recall the basic law.

Answer: (b) anti-clockwise

Explanation:
1. The face nearest the magnet must become a north pole to repel it.
2. Viewed from the magnet's side, a north-pole face has an anti-clockwise current.

Teacher's Note:
1. Recall the basic law.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. The current induced in the solenoid opposes the motion of the magnet, so the net downward acceleration is reduced.
2. This is Lenz's law, which explains the assertion.

Teacher's Note:
1. Induced current opposes the motion.

Answer: (d) X-ray crystallography

Explanation:
1. X-ray crystallography uses diffraction.
2. The others are applications of eddy currents.

Teacher's Note:
1. Recall the basic law.

Answer: (c) B l v sin θ

Explanation:
1. Only the component of \( v \) perpendicular to the rod, \( v \sin \theta \), cuts the field lines.
2. So emf = \( B l v \sin \theta \).

Teacher's Note:
1. Recall the basic law.

Answer: (d) in both AD and BC

Explanation:
1. The sides AD and BC move perpendicular to their length and cut the field lines, so each has a motional emf.
2. The two emfs oppose in the loop, so no net current flows.

Teacher's Note:
1. Each cutting side has an emf.

Answer: (d) zero

Explanation:
1. The flux through the wire does not change as it rotates about its own axis, so the emf is zero.

Teacher's Note:
1. Recall the basic law.

Answer: (b) an electric generator

Explanation:
1. Rotation in a field generates an induced current, which is the principle of a generator.

Teacher's Note:
1. Recall the basic law.

Answer: (b) Faraday's law

Explanation:
1. Faraday's law of induction describes emf produced by a change of flux, including that due to motion.

Teacher's Note:
1. Recall the basic law.

Answer: (a) 1.26 V

Explanation:
1. \( \omega = 2\pi \times 0.5 = \pi \) rad/s.
2. \( e_{\max} \) = NBAω = \( 200 \times 0.02 \times 0.10 \times \pi = 1.26 V \).

Teacher's Note:
1. Recall the basic law.

Answer: (a) electromagnetic induction

Explanation:
1. Production of emf by a changing flux is electromagnetic induction.

Teacher's Note:
1. Recall the basic law.

Answer: (b) \( -\frac{n(W_2-W_1)}{5Rt} \)

Explanation:
1. \( e = -n(W2 - W1)/t \).
2. The total resistance is \( R + 4R = 5R \), so I = -n(W2 - W1)/(5Rt).

Teacher's Note:
1. Recall the basic law.

Answer: (d) III only

Explanation:
1. The emf exists only as long as the flux continues to change.

Teacher's Note:
1. Recall the basic law.

Answer: (d) eddy currents, oppose, quickly

Explanation:
1. Eddy currents in the core oppose the motion (Lenz's law) and bring the coil to rest quickly.

Teacher's Note:
1. Recall the basic law.

Answer: (c) counter clockwise

Explanation:
1. The increasing clockwise current increases the inward (into the page) flux through the inner loop.
2. The induced current produces an opposing field, so it is counter clockwise.

Teacher's Note:
1. Recall the basic law.

Answer: (c) eddy currents

Explanation:
1. Strong eddy currents heat and melt the metal.

Teacher's Note:
1. Recall the basic law.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. \( L = \mu_{0} N^{2} A/l \), so doubling \( N \) multiplies \( L \) by four.
2. The reason gives the correct explanation.

Teacher's Note:
1. \( L \) is proportional to \( N^{2} \).