Q. 135.0( 3 Votes )
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.
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, 
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