Question

A circular loop carrying a current i has wire of total length L. A uniform magnetic field B exists parallel to the plane of the loop. (a) Find the torque on the loop. (b) If the same length of the wire is used to form a square loop, what would be the torque ? Which is larger ?

Answer 1

(a) Radius = r,

Circumference = $L=2\pi r$

So $a=\frac{L^2}{4\pi }$

$\tau =niaB=\frac{i{L}^{2}B}{4\pi }$

(b) $4s=L\Rightarrow s=\frac{L}{4}$

area = ${\left(\frac{L}{4}\right)}^2=\left(\frac{L^2}{16}\right)$

$\tau =niaB=\frac{i{L}^{2}B}{16}$