Shows a circular wire-loop of radius a m carrying a current I, placed in a perpendicualr matgnetic 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. Find the force of compression in the wire.

Explanation

(a) (i)

`dl = a d theta`
`dF = Bidl = Bi a d theta`
(ii) Compression in the wire
`C = B i a`
Note: Check short cut for how to calculate tension/compression in the ring.
(b)
Strain `in = (Delta L)/(L) = (2pi Delta a)/(2 pi a) = (Delta a)/(a)`
Stress `sigma = (C )/(A) = (Bia)/(pi r^(2))`,
where `A`: area of cross-section of wire.
`Y = (sigma)/(in) = (Bia//pi r^(2))/(Delta a//a)`
Change in the radius of ring
`Delta a = (Bia^(2))/(pi r^(2) Y)`