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 ) .

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 &#62; &#62; a ) . The magnitude of the torque on the loop about z -axis is given by.

Quantrex Academy · Accepted Answer

Correct answer: C. 2 &#956; 0 I a 2 2 &#960; b

Net force acting on wire AB & CD are zero F 1 = I L B = I &#215; 2 a &#215; &#956; 0 I 2 &#960; a 2 + b 2 = &#956; 0 I 2 a &#960; a 2 + b 2 &#964; = F 1 cos&#952; &#215; 2 a = &#956; 0 I 2 a &#960; a 2 + b 2 &#215; b a 2 + b 2 &#215; 2 a &#964; = 2 &#956; 0 I 2 a 2 b &#960; a 2 + b 2 &#8776; 2 &#956; 0 I 2 a 2 &#960; b , &#160; &#160; a &#8810; b

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.

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