Question -
Answer -
Radius of circular coil = R
Number of turns on the coil= N
Current in the coil = I
Magnetic field at a point on itsaxis at distance x is given by the relation,
Where,
= Permeability of free space
(a) If themagnetic field at the centre of the coil is considered, then x =0.
This is the familiar result formagnetic field at the centre of the coil.
(b) Radii oftwo parallel co-axial circular coils = R
Number of turns on each coil= N
Current in both coils = I
Distance between both the coils= R
Let us consider point Q atdistance d from the centre.
Then,one coil is at a distance of 
from point Q.
agnetic field at point Q isgiven as:
Also, the other coil is at a distance of 
from point Q.
Magnetic field due to this coilis given as:
Total magnetic field,
Hence, it is proved that thefield on the axis around the mid-point between the coils is uniform.