Class 10 > Unit # 16: Electromagnetism > Mutual Induction

Talha's Physics Academy

Mutual Induction and Mutual Inductance

Mutual Induction

"The phenomenon in which a changing current in one coil (primary coil) induces an electromotive force (EMF) in a neighboring coil (secondary coil) is called mutual induction."

Consider two coils placed close to each other. The coil connected to a source of EMF is designated as the primary coil, while the other connected to a galvanometer or load is the secondary coil. Some of the magnetic flux produced by the current in the primary coil links with the secondary coil. When the current in the primary changes with time, the magnetic flux through the secondary changes, inducing an EMF in it.

Mathematical Relation for Induced EMF

The induced back EMF ($\mathcal{E}_s$) in the secondary coil is directly proportional to the time rate of change of current ($\Delta I_p / \Delta t$) in the primary coil:

$$\mathcal{E}_s = -M \frac{\Delta I_p}{\Delta t}$$

Where $M$ represents the mutual inductance of the two coils, and the negative sign reflects Lenz's Law.

Mutual Inductance

"Mutual inductance is the measure of the ability of a coil system to induce a back EMF in a secondary coil due to a changing current in the primary coil."

It is formally defined as the ratio of the induced EMF in the secondary coil to the rate of change of current through the primary coil:

$$M = -\frac{\mathcal{E}_s}{\Delta I_p / \Delta t}$$

Factors on which Mutual Inductance Depends:

• Number of turns in both coils ($N_p$ and $N_s$)
• Cross-sectional area of the coils
• Closeness (coupling coefficient) between the coils
• Nature of the core material (e.g., iron core vs. air core)

Unit of Mutual Inductance: The Henry

The SI unit of mutual inductance is the Henry ($\text{H}$).

Definition of 1 Henry: The mutual inductance of a coil pair is said to be $1\text{ Henry}$ if a current varying through the primary coil at the rate of $1\text{ ampere per second}$ induces a back EMF of $1\text{ volt}$ in the secondary coil.

Fig: Mutual induction setup showing primary coil with current source and secondary coil connected to a galvanometer.

© 2026 Talha's Physics Academy. All rights reserved.