20.3 MUTUAL INDUCTANCE AND SELF-INDUCTANCE

This section explores two related electromagnetic phenomena: self-induction, where a coil induces an electromotive force (emf) in itself, and mutual induction, where a changing current in one coil induces an emf in a nearby coil.

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Key Concepts

Self-Induction

• Definition: The phenomenon in which a changing current in a coil induces an electromotive force (emf) in the coil itself.
• Mechanism: A change in current ($\Delta I$) within a coil over a time interval ($\Delta t$) causes a change in the magnetic field and thus a change in magnetic flux through the coil. This changing flux induces an opposing emf ($\varepsilon_L$) in the same coil.
• Back EMF: The self-induced emf is often called "back emf" because, according to Lenz's law, it always opposes the change in current that created it.
• Inductors: Coils designed to have a specific self-inductance are called inductors or chokes. They are fundamental components in AC circuits, where they function similarly to resistors in controlling current.

Figure 20.9 (a): Self-induction in a coil connected to a battery and rheostat.

Mutual Induction

• Definition: The phenomenon in which a changing current in one coil (the primary coil) induces an emf in a neighboring coil (the secondary coil).
• Mechanism: When an alternating or changing current flows through the primary coil, it produces a changing magnetic flux. If a secondary coil is placed nearby, this changing flux links with it, inducing an emf in the secondary coil.
• The induced emf in the secondary coil ($\varepsilon_2$) is proportional to the rate of change of current in the primary coil ($\Delta I_1 / \Delta t$).

Figure 20.9 (b): Mutual induction between two coils.

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Summary

• Self-Induction: A changing current in a coil induces an opposing emf in the same coil. This property is quantified by self-inductance (L).
• Mutual Induction: A changing current in one coil induces an emf in a nearby coil. This is quantified by mutual inductance (M).
• Lenz's Law: In both cases, the negative sign in the formulas signifies that the induced emf opposes the change that causes it.
• Inductors: Components that utilize self-inductance are called inductors and are crucial in AC circuits.
• Unit: The SI unit for both self-inductance and mutual inductance is the henry (H).

Real-World Application: Inductance is a fundamental principle behind transformers, electric motors, generators, and various electronic filters and oscillators.

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References

(Derived from FBISE textbook)