A current-carrying circular coil of magnetic moment M is...

A current-carrying circular coil of magnetic moment $M$ is situated in a magnetic field $B$. The work done in deflecting it from an angle $0^\beta$ to $\theta^{\circ}$ will be
(a) $M B$
(b) $M B(1-\cos \theta)$
(c) $-M B$
(d) $M B(1-\sin \theta)$

Key Concepts

Magnetic Moment

Magnetic moment is a measure of the strength and orientation of a magnetic source. In the context of a current-carrying loop, it quantifies how the loop interacts with an external magnetic field, determining the torque and potential energy experienced by the loop.

Torque on a Magnetic Dipole

When a magnetic dipole (such as a current-carrying coil) is placed in a magnetic field, it experiences a torque that tends to align the dipole with the magnetic field. This torque is given by the cross product of the magnetic moment and the magnetic field, and its magnitude is MB sin(theta), where theta is the angle between the magnetic moment and the magnetic field.

Potential Energy of a Magnetic Dipole

The potential energy associated with a magnetic dipole in a magnetic field is determined by the orientation of the dipole relative to the field. It can be expressed as U = -M·B or specifically as -MB cos(theta). This potential energy changes as the dipole rotates, leading to an energy difference used to calculate the work done.

Work Done in Rotational Motion

Work done during the rotation of a magnetic dipole in a magnetic field is related to the change in its potential energy. When the dipole rotates from one angle to another, the work done is equal to the difference in potential energy, which in this case can be expressed as MB(1 - cos(theta)) when rotating from an initial angle of zero.

Please give Ace some feedback