Multiple choice

A square loop of side 10 cm and resistance 1 ohm is moved towards right with a constant velocity v. The left arm of the loop is in a uniform magnetic field of 2T. The field is perpendicular to the plane and is coming out of it. The loop is connected to a network of resistors each of value 3 ohm. With what speed should the loop be moved so that a steady current of 1 mA flows in the loop?

  1. 50 m/sec

  2. 5 m/sec

  3. 2 cm/sec

  4. 80 cm/sec

  5. 12.5 m/sec
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C Correct answer
Explanation

The network of resistors forms a balanced Wheatstone bridge,  and hence resistor of 3 ohm in the middle can be neglected. Remaining resistors have an equivalent resistance = 3 ohm. Total resistance = 3 + 1 = 4 ohm. Induced emf, Bvl = IR Or 2 x v x 0.10 = 1 x 10- 3 x 4. This gives v = 2 cm/sec.

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