A hypothetical magnetic field existing in a region is given by , where denotes the unit vector along the radial direction. A circular loop of radius 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.

Question

Philoid · Accepted Answer

Given-
hypothetical magnetic field exists in a region,

Where

, is a unit vector along the radial direction a.

It is a circular loop of radius a

So, the length of the loop,

Electric current through loop = i

Also, the loop is placed with its plane parallel to the X−Y plane and its centre lies at (0,0, d).

The angle between the length of the loop l and the magnetic field B is θ

Magnetic force is given by

where,

B= magnetic field

I = current

l = length of the wire

and θ = the angle between B and l

Substituting the values -

Looking into the fig,