A circular loop of radius r carrying a current i is held at the centre of another circular loop of radius R(gtgtr) carrying a current I. The plane of the smaller loop makes an angle of `30^@` with that of the larger loop. It 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 this force?

Explanation

Magnetic field at centre due to loop of radius `R`.,
`B = (mu_(0) i_(0))/(2R)`, perpendicular to plane of loop
Magnetic moment of smaller loop
`M = i.pi r^(2)`, perpendicular to plane of loop
`M` is `_|_^(ar)` to `B`
Torque acting on the smaller loop
`tau = MB sin theta = MB, theta = 90^(@)`
`= i pi r^(2).(mu_(0)i_(0))/(2R)`
`= (mu_(0)i_(0) i pi r^(2))/(2R)`