Two concentric coplanar circular conducting loops have radii $R$ and $r(R \gg r)$. Their mutual inductance is proportional to

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Aicharya · Accepted Answer

Let us consider a coil having $N_1$ turns and radius $r$ is surrounded by another coil having $N_2$ turns and of radius $R$ as shown in the figure below, Magnetic field due to coil 2 at the centre, $B_2=\frac{\mu_0 N_2 I}{2 R}$ Magnetic flux through the coil, $\phi_{B_1}=N_1 B_2 A=\frac{N_1 \mu_0 N_2 I \cdot \pi r^2}{2 R}$ But, $\phi_{B_1}=M I$ From Eqs. (i) and (ii), we get $M I=\frac{N_1 \mu_0 N_2 I. \pi r^2}{2 R} \Rightarrow M=\frac{N_1 \mu_0 N_2 \cdot \pi r^2}{2 R} \Rightarrow M \propto \frac{r^2}{R}$

Two concentric coplanar circular conducting loops have radii \(R\) and \(r(R \gg r)\). Their mutual…

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