If a bar magnet in magnetic moment $m$ is deflected from an angle $θ$ in a uniform magnetic field of induction $B$ , the work done in reversing the direction is

Question

Verified by Toppr

Answer 1

Now lets assume that the bar magnetic is initially placed parallel to the field the initial potential energy will be $U_{i} = - M . B = - M B cos 0 = - M B$
Now when it is deflected by an angle $θ$ then $U_{f} = - M . B = - M B cos θ$
Now we know that the work done = $- Δ U$
$Δ U = U_{i} - U_{f}$
$Δ U = - M B (1 - cos θ)$
therefore, work done $= M B (1 - cos θ)$ .

Answer 2

Now lets assume that the bar magnetic is initially placed parallel to the field the initial potential energy will be

U_{i} = - M . B = - M B cos 0 = - M B

Now when it is deflected by an angle

θ

then

U_{f} = - M . B = - M B cos θ

Now we know that the work done =

- Δ U

Δ U = U_{i} - U_{f}

Δ U = - M B (1 - cos θ)

therefore, work done

= M B (1 - cos θ)

.