Question

The figure 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) $F_{dl}=i.(dl\times B)=idlB$

(because dl and B are perpendicular to each other)

(b) 2T sin $\theta =i.(dl\times B)$

$2Tsin\theta =idlB$

$\therefore \theta$ is very small, sin $\theta =\theta$

$dl=a\times 2\theta$

$2T\theta =i.2a\theta B$

T=iaB