Question

Two closely wound circular coils have the same number of turns, but one has twice the

radius of the other. How are the self-inductances of the two coils related? Explain your

reasoning.

Answer 1

Answer

Self inductance of cool is given by

$L=\frac{\mu_0N^2\pi r^2}{l}$

Now of first coil

$L_1=\frac{\mu_0N^2\pi r_1^2}{l}$

Now for second coil

$r_2=2r_1$

So $L_2=\frac{\mu_0N^2\pi r_2^2}{l}\\$

$L_2=4L_1$

This is relationship between both coil.