Module 3 : MAGNETIC FIELD
Lecture 14 : Potential Energy of a Magnetic Dipole
Potential Energy of a Magnetic Dipole

A current loop does not experience a net force in a magnetic field. It however, experiences a torque. This is very similar to the behaviour of an electric dipole in an electric field. A current loop, therefore, behaves like a magnetic dipole.
We define the magnetic dipole moment $\vec\mu$of a current loop to be a vector of magnitude

\begin{displaymath}\mid\mu\mid = IA\end{displaymath}

and direction perpendicular to the plane of the loop (as determined by right hand rule). If the loop has $N$turns, $\mid\mu\mid = NIA$. In a magnetic field, the dipole experiences a torque

\begin{displaymath}\vec\tau = \vec\mu\times\vec B\end{displaymath}

The form of torque suggests that in a magnetic field the dipole tends to align parallel to the field. If the orientation of the dipole is at some angle $\theta$to the field, there must be some potential energy stored in the dipole. This is because, if we wish to bring the dipole from $\theta=0$to some arbitrary angle $\theta$, we have to oppose the torque due to the field and do work in the process.

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