A hypthetical magnetic field existing in a region is given by `vecB= B_0 vece_r,` where `vec_r` denotes the uit vector along the redial direction. A circular loop of radus a, carrying a current I, is placed with its plane parallel to the x-y plane and the centre at (0,0, d) .Find the magnitude of the magnetic force acting on the loop.

Explanation

(a)
Consider a small length `dl` of wire
`dF = Bi dl`, downward
Force on each element is in downward direction
`F = int dF = Bi int dl = Bi.2pi a`, downward
(b)
Resolving magnetic field into `B_(0) cos theta` and `B_(0) sin theta`, the loop is equivalent to

In Fig. (i), magnetic force on loop is zero
In Fig. (ii) magnetic force
`F = B_(0) sin theta i.2 pi a`
`= B_(0) (ai)/(sqrt(a^(2) + d^(2))).2 pi a`
`= (2pi B_(0) i a^(2))/(sqrt(a^(2) + d^(2)))`