If a magnetic dipole of dipole moment M rotated through an angle θ 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 θ with respect to the direction of the field H , then the work done is : (A)  MH sin θ  (B)  MH (1 − sin θ)  (C)  MH cos θ  (D)  MH (1 − cos θ)

Tardigrade Admin · Accepted Answer

When a magnetic dipole of dipole moment

M

is rotated through an angle

θ

with respect to the direction of the field

H

, then work done is done. This work is stored as magnetic potential energy in the dipole. The potential energy of a magnetic dipole of magnetic moment

M

placed in magnetic field

H

is

U_{θ} = - M \cdot H = - M H cos θ

where

θ

is angle between the vector

M

and

H

. Initially the dipole possesses minimum potential energy

U_{0}

,therefore work required to turn through angle

θ

is

W = U_{θ} - U_{0} = - M H cos θ - (- M H cos θ)

= - M H cos θ + M H

∴ W = M H (1 - cos θ)

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

$M H s in θ$

$M H (1 - s in θ)$

$M H cos θ$

$M H (1 - cos θ)$

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

MHsinθ

MH(1−sinθ)

MHcosθ

MH(1−cosθ)

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

$M H s in θ$

$M H (1 - s in θ)$

$M H cos θ$

$M H (1 - cos θ)$