A circular loop of radius r carrying a current i is held at the center of another circular loop of radius R (r) carrying a current I. The plane of the smaller loop makes and angle of 30° with that of the larger loop. If the smaller loop is held fixed in this position by applying a single force at a point on its periphery, what would be the minimum magnitude of the force?

Question

A circular loop of radius r carrying a current i is held at the center of another circular loop of radius R (>>r) carrying a current I. The plane of the smaller loop makes and angle of 30° with that of the larger loop. If the smaller loop is held fixed in this position by applying a single force at a point on its periphery, what would be the minimum magnitude of the force?

Philoid · Accepted Answer

Given:

Current carried by circular loop of radius r = i

Current carried by circular loop of radius R(>>r) = I

Angle between the planes of the two loops = 30⁰

Diagram:

Formula used:

Magnetic field at the center of a circular loop of radius r

M= ,

where

I = current through the loop,

r = radius of the circle,