Conducting Bar Across R1 & R2

A conducting bar PQ is free to slide on two parallel conducting rails as shown in figure. Two resistors R1 and R2 are connected across the ends of the rails. There is a uniform magnetic field B pointing into the page. An external agent pulls the bar to the left at a constant speed v. The correct statement about the directions of induced currents I1 and I2 flowing through R1 and R2 respectively is:

(A) I1 is in anticlockwise direction and I2 is in clockwise direction
(B) Both I1 and I2 are in anticlockwise direction
(C) Both I1 and I2 are in clockwise direction
(D) I1 is in clockwise direction and I2 is in anticlockwise direction

Solution

As PQ moves leftwards, the area of loop ABQP decreases causing reduction in flux. So, the direction of current through R1 should be such that the flux can be increased. An upward current through R1 helps to strengthen the magnetic field. Upward current through R1 is the clockwise current through the left loop.

As PQ moves leftwards, the area of loop A’B’QP increases causing increase in flux. So, the direction of current through R2 should be such that the flux can be decreased. An upward current through R2 helps to weaken the magnetic field. Upward current through R2 is the anticlockwise current through the right loop.

Hence, Option (D).

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