Module 3 : MAGNETIC FIELD
Lecture 19 : Mutual Inductance

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Analogously, we can argue that if the second loop carries a current $I_2$which is varied with time, it generates an induced emf in the first coil given by \begin{displaymath}{\cal E}_1 = -M_{12}\frac{dI_2}{dt}\end{displaymath}

For instance, consider two concentric solenoids, the outer one having $n_1$turns per unit length and inner one with $n_2$turns per unit length. The solenoids are wound over coaxial cylinders of length $L$each. If the current in the outer solenoid is $I_1$, the field due to it is $B_1=\mu_0n_1I_1$, which is confined within the solenoid. The flux enclosed by the inner cylinder is

\begin{eqnarray*} N_2 \Phi_2 &=& N_2\pi r_2^2B_1 \\ &=& n_2L\pi r_2^2\cdot(\mu_0n_1I_1)\\ &=& \mu_0n_1n_2L\pi r_2^2I_1 \end{eqnarray*}

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