# Numerical Problems : Electromagnetic Induction

#### LEVEL – I

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.

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 ?

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?

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

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.

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.

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 ? 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.

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.

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