Module 3 : MAGNETIC FIELD
Lecture 19 : Mutual Inductance

The flux enclosed by the second loop, (called the secondary ) is

\begin{eqnarray*} \Phi_2 &=& \int_{S_2}\vec B_1\cdot\vec{dS_2}\\ &=& \int_{S_2... ...I_1}{4\pi}\oint\oint\frac{\vec{dl_1}\cdot\vec{dl_2}}{\mid r\mid} \end{eqnarray*}

Clearly,  \begin{displaymath}M_{21} = \frac{\mu_0}{4\pi}\oint\oint\frac{\vec{dl_1}\cdot\vec{dl_2}}{\mid r \mid}\end{displaymath}

It can be seen that the expression is symmetric between two loops. Hence we would get an identical expression for $M_{12}$. This expression is, however, of no significant use in obtaining the mutual inductance because of rather difficult double integral.
Thus a knowledge of mutual inductance enables us to determine, how large should be the change in the current (or voltage) in a primary circuit to obtain a desired value of current (or voltage) in the secondary circuit. Since $M_{21}=M_{12}$, we represent mutual inductance by the symbol $M$. The emf ${\cal E}_s$in the secondary circuit is given by  \begin{displaymath}{\cal E}_s = -M\frac{dI_p}{dt}\end{displaymath} , where $I_p$is the variable current in the primary circuit.
Units of $M$is that of Volt-sec/Ampere which is known as Henry (h)

Example 22    Example 23    Exercise 1   Exercise 2

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