A circular loop of wire having a radius of 8.0 cm carries a current of 0.20 A. A unit vector parallel to the dipole moment of the loop is given by . If the loop is located in a magnetic field given in T by , we have to find (a) torque on the loop and (b) the magnetic potential energy of the loop.

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(a)

The unit vector parallel to the dipole moment of the loop is

.

Loop is a circular wire of radius 8.0 cm. The area of the loop is

.

Current flowing in the loop

.

Therefore, the magnitude of the magnetic dipole moment of the current carrying loop is

The magnetic dipole moment is

The current carrying loop is placed in a magnetic field

.

Therefore, the torque on the loop will be

(b)

The magnetic potential energy of the loop