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Question:

A circular coil having N turns and radius r carries a current I. It is held in the XZ plane in a magnetic field Bî. The torque on the coil due to the magnetic field is

Bπr²IN

Br²IπN

Bπr²IN

Zero

Solution:

Correct option is A. Bπr²IN
Magnetic moment of coil = NIÂj = NI(πr²)ĵ
Torque on loop (coil) = M→ × B→ = NI(πr²)Bsin 90°(-k^) = NIπr²B(-k^).