Question

The mutual inductance $M_{12}$ of coil $1$ with respect to coil $2$

• A. increases when they are brought nearer.
• B. is the same as $M_{21}$ of coil $2$ with respect to coil $1$.
• C. increases when one of them is rotated about an axis.
• D. depends on the current passing through the coils.

Answer 1

Answer: (A), (B)

is the same as $M_{21}$ of coil $2$ with respect to coil $1$.

The mutual inductance of the coils is given by

$M_{12}=M_{21}=\frac{{\mu }_0{n}_1{n}_2\pi r^2}{l}$

As the area of cross section of the coil $\left(\pi r^2\right)$ and length $\left(l\right)$ is common. And $n_1$and $n_2$ are no of turns in the coils.

Therefore, $M_{21}=M_{12}$

But as we bring the coils near, number of field lines associated with each other increases. Hence, mutual inductance increases.

According to the given formula mutual inductance does not depend on the current through the coil and rotation of the coil.

Final answer: Option (a), (d)