Question

shows a circular wire-loop of radius a, carrying a current i, placed in a perpendicular magnetic field B. (a) Consider a small part dl of the wire. Find the force on this part of the wire exerted by the magnetic field. (b) Find the force of compression in the wire.

Answer 1

(a) $Fdl=i\times dl\times B$ towards centre. (By cross product rule)

(b) Let the length of subtends an small angle of $2\theta$ at the centre

Here,

$2T\sin \theta =i\times dl\times B$

$2T\theta =i\times a\times 2\theta \times B$ [As $\theta \to 0,\sin \theta \approx 0$]

$T=i\times a\times B$

$T=aiB$

Force of compression on the wire $=iaB$