Q. Two coils of self inductance $L_{1}$ and $L_{2}$ are placed closer to each other so that total flux in one coil is completely linked with other. If $M$ is mutual inductance between them, then
A) $M = L_{1}L_{2}$
B) $M = L_{1}/L_{2}$
C) $M = \sqrt{L_{1}L_{2}}$
D) $M = \left( L_{1}L_{2} \right)^{2}$
Explanation
(c) $M = - \frac{e_{2}}{di_{1}/dt} = - \frac{e^{2}}{di_{2}/dt}$
Also $e_{1} = - L_{1}\frac{di_{1}}{dt}.\ e_{2} = - L_{2}\frac{di_{2}}{dt}$
$M^{2} = \frac{e_{1}e_{2}}{\left( \frac{di_{1}}{dt} \right)\left( \frac{di_{2}}{dt} \right)} = L_{1}L_{2} \Rightarrow M = \sqrt{L_{1}L_{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.