If a magnetic dipole of dipole moment M rotated through an angle $ heta$ with respect to the direction of the field H, then the work done is

Question

If a magnetic dipole of dipole moment M rotated through an angle $	heta$ with respect to the direction of the field H, then the work done is

Dr. Abubacker · Accepted Answer

(d) The potential energy of a magnetic dipole of magnetic moment M placed in magnetic field H is given as
$U_{	heta} = - \mathbf{M.H} = - MH\cos	heta$
Where $	heta$ is angle between the vector M and H. Initially the dipole possesses minimum potential energy $U_{0},$ therefore work requires to turn through angle $	heta$ is
$W = U_{	heta} - U_{0}$
$\ \ \ \ \ \  = - MH\cos{	heta - ( - MH\cos	heta)}$
$\ \ \ \ \ \  = - MH\cos{	heta + MH}$
$W = MH(1 - \cos	heta)$

Q. If a magnetic dipole of dipole moment M rotated through an angle $\theta$ with respect to the direction of the field H, then the work done is

Explanation

Reviewed by Dr. Abubacker

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