Question

A circular loop of radius $a$, carrying a current $i$, is placed in a two-dimensional magnetic field. The centre of the loop coincides with the center of the field. The strength of the magnetic field at the periphery of the loop is $B$. Find the magnetic force on the wire.

Answer 1

Radius is a, so length of loop $=2\pi a$

Current in loop $=i$

$|\overrightarrow{F}|=i\overrightarrow{l}\times \overrightarrow{B}$

$|\overrightarrow{F}|=i2\pi aB$

(as angle between loop and magnetic field is ${90}^0$)

The direction can be found using FLeming's Left hand rule, ie, Perpendicular to plane of figure and inward direction.