Question

A circular loop carrying a current i is made of a wire of 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

Given,
Magnetic field intensity = B 
Circumference, L = 2πr, where r is the radius of the coil.
So, area of the coil,A =`(l^2)/(4pi`
Magnitude of current = i
Torque acting on the coil,
τ = niABsinθ, where θ is the angle between the area vector and the magnetic field.
`τ = niAB = (i L^2 B)/(4pi)`
(b) Let s be the length of the square loop.
`4s = L`
⇒ ` = (L/4^2)` =`((2l^2)/16)`

So, the torque on the circular loop is larger.