Question

Consider two coplanar, co-centric circular coils having radius r₁ and r₂ (r₂ > r₁) as shown in the figure. The mutual inductance between these two coils will be

(1) \(\frac{μ_0\pi r^2_1}{2r_2}\) 

(2) \(\frac{μ_0\pi r_1}{2r_2}\)

(3) \(\frac{μ_0\pi r^2_2}{2r_2}\)

(4) \(\frac{μ_0\pi r^2_1}{2r_1}\)

Answer 1

(1) \(\frac{μ_0\pi r^2_1}{2r_2}\) 

We will consider the bigger coil as the primary coil. In the expression

ϕ_s = B_p.A_s

we put the value of B at the center of the bigger coil.