A U-shaped wire PQRS of mass m carrying a current i is stationary above the surface of the earth in the region of a uniform magnetic field B directed into the page as shown in Fig. Then
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a
i=mgl2B
b
i=mg2l2B
c
i=mg2l1+l2B
d
i=mg2l1−l2B
answer is A.
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Detailed Solution
Refer to Fig. It follows from Fleming's left hand rule that the wire segment PQ experiences a force F1 = B i l1 directed to the right and the wire segment SR experiences an equal force F1 = B il1 but directed to the left. These forces cancel each other. The wire segment QR experiences a force F = Bil2 directed vertically upward. The wire frame will remain stationary in air if F equal the weight mg of the wire frame, i.e. Bil2=mg⇒ i=mgl2B which is choice (a).