Q.

A wire cd of length l and mass m is sliding without friction on conducting rails ax and by as shown. The vertical rails are connected to each other with a resistance R between a and b. A uniform magnetic field B is applied perpendicular to the plane abcd such that cd moves with a constant velocity of

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a

mgRBl

b

mgRB2l2

c

mgRB3l3

d

mgRB2l

answer is B.

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Detailed Solution

Due to magnetic field, wire will experience an upward force   F=Bil=B BvlR l⇒F=B2vl2RIf wire slides down with constant velocity then F=mg⇒B2vl2R=mg⇒v=mgRB2l2
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A wire cd of length l and mass m is sliding without friction on conducting rails ax and by as shown. The vertical rails are connected to each other with a resistance R between a and b. A uniform magnetic field B is applied perpendicular to the plane abcd such that cd moves with a constant velocity of