Module 3 : MAGNETIC FIELD
Lecture 19 : Mutual Inductance
Mutual Inductance

According to Faraday's law, a changing magnetic flux in a loop causes an emf to be generated in that loop. Consider two stationary coils carrying current. The first coil has $N_1$turn and carries a current $I_1$. The second coil contains $N_2$turns. The current in the first coil is the source of a magnetic field $\vec B_1$in the region around the coil. The second loop encloses a flux $N_2\Phi_2 = N_2\int_S\vec B_1\cdot\vec{dS_2}$, where $S$is the surface of one turn of the loop. If the current $I_1$in the first coil is varied, $\vec B_1$, and consequently $\Phi_2$will vary with time.

The variation of $\Phi_2$causes an emf to be developed in the second coil. Since $B_1$is proportional to $I_1$, so is $\Phi_2$. The emf, which is the rate of change of flux is, therefore, proportional to $dI_1/dt$,  \begin{displaymath}{\cal E}_2 = -M_{21}\frac{dI_1}{dt}\end{displaymath}

where $M_{21}$is a constant, called the mutual inductance of the two coils, which depends on geometrical factors of the two loops, their relative orientation and the number of turns in each coil.

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