Self and Mutual Inductance

Problems from IIT JEE

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

  1. maximum is situation (i).
  2. maximum is situation (ii).
  3. maximum is situation (iii).
  4. 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).