# Self and Mutual Inductance

## Problems from IIT JEE

**Problem (IIT JEE 2001): **
Two circular coils can be arranged in any of the three situations shown in figure. Their mutual inductance will be

- maximum is situation (i).
- maximum is situation (ii).
- maximum is situation (iii).
- the same in all situations.

**Solution: **
The mutual inductance $M$ is given by, $\phi=Mi$, where $\phi$ is the flux through a coil due to the current $i$ in another coil. The flux through an area $\vec{A}$ due to a magnetic field $\vec{B}$ is given by $\phi=\vec{B}\cdot\vec{A}$. The $\vec{B}$ and $\vec{A}$ are parallel in configuration (i) but perpendicular in configuration (ii) and configuration (iii). Hence, the flux and mutual inductance are maximum in configuration (i).