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Question

Two conducting rings P and Q of radii and r and 2r rotate uniformly in opposite directions with centre of mass velocities 2 v and v respectively on a conducting surface S. There is a uniform magnetic field of magnitude B perpendicular to the plane of the rings. The potential difference between the highest points of the two rings is
1030018_560d5c7868864d79b51f9db0ace5e440.png

A
(a) zero
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B
(b) 4 Bvr
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C
(c) 8 Bvr
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D
(d)16 Bvr
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Solution

The correct option is C (c) 8 Bvr
Effective length moving in magnetic field is 2r and 4r respectively.

E1=B(2r)(2v)=4Bvr

Er=B(4r)(v)=4Bvr

To find the potential difference, we replace the induced emfs in the rings by cells.

Potential Difference =E1+E2=8Bvr

1000642_1030018_ans_c5da6b35656d49b0a2fb1e8f09138c1d.png

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