Question

There is a pair of concentric and coplanar conducting loops of radii R₁ and R₂ such that R₂ = 0.01 R₁. To which of the following is the mutual inductance M for this pair directly proportional? 

A. 1/R\(^2_1\) 

B. R\(^2_1\)

C. 1/R₁ 

D. R₁

Answer 1

Correct option is D. R₁

R₂ = 0.01 R₁

\(M=\frac{\mu_0}{2R_1}\pi R^2_2\,N_1N_2\)

Mutual inductance \(M=\frac{\mu_0}{2R_1}\pi R^2_2\)

\(M=\frac{\pi_0}{2\,R_1}\pi(0.01R_2)^2\)

\(M=\frac{\mu_0}{2R_1}\pi\times0.0001\,R^2_1\)

\(M=\frac{\mu_0\pi}{2}\times0.0001\,R^2_1\)

\(M\,\alpha \,R_1\)