Question

two coaxial circular coils of radii A and B are separated by large distance x and carry equal currents what is the force on mutual interaction between them

Answer 1

Radius of 2 parallel co-axial circular coil = R

Number of turns = N

Current in both coils = I

Distance between the 2 coils = 2R

As the point where we have to find the magnetic field is half way between the 2 coils, it will be at a distance of R from center of both the coils.

So the magnetic field at the point because of coil 1 = B1

So, B1 = (μoNIR2) / 2[(R+R)2+R]3/2

Similarly, B2 = (μoNIR2) / 2[(R+R)2+R]3/2

So, the total magnetic field, B = B1 + B2

B = B1 + B2

= (μoNIR2) / 2[(R+R)2+R]3/2 + (μoNIR2) / 2[(R+R)2+R]3/2

= (μoNIR2) / [(R+R)2+R]3/2

= (μoNIR2) / [4R2+R] 3/2

= (μoNIR2) /8R3[1+1/R]3/2

Since, R>>1 we can say

B = (μoNIR2) /8R3