Question

The work done in moving a unit n-pole around a current carrying straight wire, in a circle of radius $10$ $cm$ is $w$. The work done in moving it in a circle of radius $20$ $cm$ is:

• A. $w$
• B. $2w$
• C. $w/2$
• D. $4w$

Answer 1

The correct option is A $w$

$\overline{F}$ $=m_{a}g$ = $m\overline{B}$
where m = magnetic pole
$\overline{B}=\frac{\mu i}{2\pi R}$
Direction of the force is tangential to the chosen circle around which the particle is moving.
therefore,
Work Done w= $\int F.dr$
w= $\int m\frac{\mu i}{2\pi R}dr$
w= $m\frac{\mu i}{2\pi R}2\pi R$
w= $\mu mi$
which is independent of R.