# Numerical Problems : Electromagnetic Induction

#### LEVEL – I

Q:1. An inductor coil stores 32 J of magnetic energy and dissipates energy as heat at the rate of 320 W when a current of 4A is passed through it. Find the time constant of the circuit when this coil is joined across an ideal battery.

Ans: 0.2 s

Q:2. It is desired to set up an undriven L-C circuit in which the capacitor is originally charged to potential difference of 100.0 V. The maximum current is to be 1.0 A , and the oscillation frequency is to be 1000 Hz. What are the required values of L and C ?

Ans: C = 1.59 μF, L = 15.9 mH

Q:3. A circular ring of diameter 20 cm has a resistance of 0.01 Ω. How much charge will flow through the ring if it is turned from a position perpendicular to a uniform magnetic field of 2.0 T to a position parallel to the field?

Ans: 2π Coulombs.

Q:4. A coil of inductance 8.4 × 10-3 H and a resistance of 6Ω are connected to a 12 V battery as shown in the figure. Switch is closed at t = 0. At what time is the magnetic energy in the coil 4.2 × 10-3Joule ?

Ans: 0.97 ms

Q:5. An inductor-coil of inductance 20 mH having resistance 10 Ω is joined to an ideal battery of emf 5.0 V. Find the rate of change of the induced emf at t = 0.

Ans: 2.5 × 103 v/s

Q:6. An inductor-coil carries a steady-state current of 2.0 A when connected across an ideal battery of emf 4.0 V. If its inductance is 1.0 H, find the time constant of the circuit.

Ans: 0.5 s

Q:7. An average emf of 20 V is induced in an inductor when the current in it is changed from 2.5 A in one direction to the same value in the opposite direction in 0.1 s. Find the self-inductance of the inductor.

Ans: 0.4 H

Q:8. The figure shows a wire sliding on two parallel , conducting rails placed at a separation ‘ l ‘. A magnetic field B exists in a direction perpendicular to the plane of the rails. What force is necessary to keep the wire moving at a constant velocity v ?

Ans: $\displaystyle \frac{B^2 l^2 v}{R}$

Q:9. A semicircular copper rod of radius R rotates about an axis passing through one of its ends and lying in the plane of the rod with an angular speed ω in a uniform magnetic field B. Find the emf developed between the two ends of the rod. The field is perpendicular to the motion of the rod.

Ans: 2 BωR2

Q:10. A square-shaped copper coil has edges of length 50 cm and contains 50 turns. It is placed perpendicular to an extended uniform magnetic field of strength 1.0 T magnetic field . It is rotated in the magnetic field about one of its diagonal with time period 0.25 s . Find the magnitude of the value of maximum emf induced in the loop.

Ans: 100 π volt

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