Module 3 : MAGNETIC FIELD
Lecture 19 : Mutual Inductance

This equality can be proved quite generally from Biot-Savart's law. Consider two circuits shown in the figure.

\includegraphics{fig3.50a.eps}

The field at $\vec{r_2}$, due to current in the loop $C_1$(called the primary ) is \begin{displaymath}\vec B_1 = \frac{\mu_0}{4\pi}I_1\oint \frac{\vec{dl_1}\times\hat r}{\mid r\mid^2}\end{displaymath}

where $\vec r = \vec r_2 -\vec r_1$. We have seen that $\vec B_1$can be expressed in terms of a vector potential $\vec A_1$, where

, by Biot-Savart's law  \begin{displaymath}\vec A_1 = \frac{\mu_0I_1}{4\pi}\oint\frac{\vec{dl_1}}{\mid r\mid}\end{displaymath}

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