Question

Two parallel coaxial circular coils of equal radius R and equal number of turns N carry equal currents I in the same direction and are separated by a distance `2R`. Find the magnitude and direction of the net magnetic field produced at the mid-point of the line joining their centres.

Answer 1

Magnetic field induction at the mid-point due to current loop 1 is
`B_1=(mu_0)/(4pi)(2piIR^2)/((R^2+R^2)^(3//2))=(mu_0IR^2)/(2(2R^2)^(3//2))`,
acting towards right.
Magnetic field induction at the mid point due to current loop 2 is
`B_2=(mu_0IR^2)/(2(R^2+R^2)^(3//2))=(mu_0IR^2)/(2(2R^2)^(3//2))`
acting towards right.
Total magnetic field induction is
`B=B_1+B_2=(mu_0IR^2)/(2(2R^2)^(3//2))+(mu_0IR^2)/(2(2R^2)^(3//2))`
`=(mu_0IR^2)/(2sqrt2R^3)=(mu_0I)/(2sqrt2R)`