A square loop of side 2 a , and carrying current I is kept in X Z plane with its centre at origin. A long wire carrying the same current I is placed parallel to the z -axis and passing through the poi

Question

A square loop of side 2 a , and carrying current I is kept in X Z plane with its centre at origin. A long wire carrying the same current I is placed parallel to the z -axis and passing through the point ( 0 , b , 0 ) , ( b > > a ) . The magnitude of the torque on the loop about z -axis is given by.

TestHub · Accepted Answer

Net force acting on wire AB & CD are zero F 1 = I L B = I × 2 a × μ 0 I 2 π a 2 + b 2 = μ 0 I 2 a π a 2 + b 2 τ = F 1 cosθ × 2 a = μ 0 I 2 a π a 2 + b 2 × b a 2 + b 2 × 2 a τ = 2 μ 0 I 2 a 2 b π a 2 + b 2 ≈ 2 μ 0 I 2 a 2 π b , a ≪ b

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