Question 289: Electromagnetic Induction

Question

A coil of radius '$$r$$' is placed on another coil (whose radius is $$\mathrm{R}$$ and current flowing through it is changing) so that their centres coincide $$(\mathrm{R} \gg \mathrm{r})$$. If both the coils are coplanar then the mutual inductance between them is ( $$\mu_0=$$ permeability of free space)

Accepted Answer

Magnetic field, $$B=\frac{\mu_0 I}{2 R}$$
Flux passing through the coil,
$$\begin{aligned}
\phi & =\mathrm{B} 	imes \pi \mathrm{r}^2 \
	herefore \quad \phi & =\frac{\mu_0 \mathrm{I}}{2 \mathrm{R}} 	imes \pi \mathrm{r}^2
\end{aligned}$$
Mutual Inductance, $$M=\frac{\phi}{I}$$
$$	herefore \quad M=\frac{\frac{\mu_0 I}{2 R} 	imes \pi r^2}{I}=\frac{\mu_0 \pi r^2}{2 R}$$

Answer

$$\frac{\mu_0 \pi \mathrm{R}^2}{2 \mathrm{r}}$$

Answer

$$\frac{\mu_0 \pi r^2}{2 R}$$

Answer

$$\frac{\mu_0 \pi r^2}{R}$$

Answer

$$\mu_0 \pi R^2$$

Electromagnetic Induction

A coil of radius '$r' is placed on another coil (whose radius is \mathrm{R} and current flowing through it is changing) so that their centres coincide (\mathrm{R} \gg \mathrm{r}). If both the coils are coplanar then the mutual inductance between them is ( \mu_0=$ permeability of free space)

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