Question

Show that the energy of a magnetic dipole m in a magnetic field B is U--m B

Answer 1

Answer:

showm

Explanation:

Consider a dipole having magnetic moment 'm' is placed in magnetic field $\vec{B}$ then the torque exerted by the field on the dipole is

$\tau = m\times B$

$\tau=mBsin\alpha$

Now to rotate the dipole in the field to its final position the work required to be done is

$U=\int \tau d\alpha$

$U=\int mBsin\alpha d\alpha$

$U= -mBcos\alpha$

$U=-\vec{m\times \vec{B}}$

Minimum energy mB is for the case when m is anti parallel to B.

Minimum energy -mB is for the case when m is parallel to B.