Question 324: Electromagnetic Induction

Question

A coil of radius '$$\mathrm{r}$$' is placed on another coil (whose radius is '$$\mathrm{R}$$' and current through it is changing) so that their centres coincide. ( $$R > r$$ ). If both coplanar, then the mutual inductance between them is proportional to

Accepted Answer

Magnetic field at the centre $$B=\frac{\mu_0 I}{R}$$
$$\phi=$$ Magnetic flux passing through the smaller coil $$=\pi \mathrm{r}^2 \mathrm{~B}$$
$$	herefore \phi=\pi r^2 	imes \frac{\mu_0 I}{R}$$
$$	herefore M=\frac{\phi}{I}=\frac{\mu \pi r^2}{R} \quad 	herefore M \propto \frac{r^2}{R}$$

Answer

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

Answer

$$\frac{r}{R}$$

Answer

$$\frac{R}{r}$$

Answer

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

Electromagnetic Induction

A coil of radius '$\mathrm{r}' is placed on another coil (whose radius is '\mathrm{R}' and current through it is changing) so that their centres coincide. ( R > r$ ). If both coplanar, then the mutual inductance between them is proportional to

Choose the correct answer: