What is the fundamental difference between self-inductance and mutual inductance?

The fundamental difference lies in the interaction. Self-inductance describes the property of a single coil to induce an EMF within itself due to a change in its own current. It's an intrinsic property of a coil. Mutual inductance, conversely, describes the phenomenon where a changing current in one coil induces an EMF in a *separate, nearby* coil. It quantifies the magnetic coupling between two distinct circuits. Both are manifestations of electromagnetic induction, but one is internal to a single circuit, and the other is an interaction between two.

Why is the induced EMF in an inductor sometimes called 'back EMF'?

The induced EMF in an inductor is called 'back EMF' because, according to Lenz's Law, its direction is always such that it opposes the change in current that produced it. If the current is increasing, the back EMF acts to reduce it; if the current is decreasing, the back EMF acts to maintain it. This opposition makes it 'back' or counter to the change, much like a back pressure or a resistive force, though it's not a resistive force in the sense of dissipating energy.

What happens to the energy stored in an inductor when the current is switched off?

When the current through an inductor is switched off, the magnetic field collapses. The energy previously stored in this magnetic field ($U = \frac{1}{2}LI^2$) is released. This rapid release of energy can induce a very large EMF (a 'spark') across the switch terminals or in the circuit, as the inductor tries to maintain the current. This energy is typically dissipated as heat in the circuit resistance, radiated as electromagnetic waves, or used to power other components for a brief period.

Can mutual inductance exist between two coils if they are very far apart?

Theoretically, yes, but practically, it would be negligible. Mutual inductance depends on the magnetic flux linkage between the two coils. As the distance between the coils increases, the magnetic field produced by one coil that passes through the other coil diminishes rapidly. Therefore, the flux linkage becomes extremely small, leading to a very low (almost zero) mutual inductance. For significant mutual inductance, the coils need to be in close proximity and appropriately oriented.

How does the core material affect the self-inductance of a coil?

The core material significantly affects the self-inductance by altering the magnetic permeability ($mu$) inside the coil. If the coil has an air core, its permeability is $mu_0$. If a ferromagnetic material (like iron) is inserted into the core, its relative permeability ($mu_r$) can be very high (hundreds or thousands). Since $L \propto \mu$, a ferromagnetic core dramatically increases the magnetic flux for a given current, and thus greatly increases the self-inductance of the coil. This is why chokes and transformers often use iron cores.

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Self and Mutual Inductance

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Version 1Updated 22 Mar 2026

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Self-inductance is the property of a coil or circuit element to oppose any change in the current flowing through it. This opposition arises due to the generation of an induced electromotive force (EMF) within the coil itself, which, according to Lenz's Law, acts to counteract the change in magnetic flux caused by the changing current. Mutual inductance, on the other hand, describes the phenomenon …

Quick Summary

Self and mutual inductance are fundamental concepts in electromagnetic induction. Self-inductance ( $L$ ) is the property of a single coil to oppose changes in its own current by inducing a 'back EMF' within itself.

This occurs because a changing current creates a changing magnetic flux through the coil, which, by Faraday's and Lenz's laws, induces an opposing EMF. The self-inductance of a solenoid is given by $L = \mu_0 \frac{N^2 A}{l}$ .

An inductor stores energy in its magnetic field, quantified by $U = \frac{1}{2}LI^2$ . Mutual inductance ( $M$ ) describes the magnetic coupling between two separate coils. A changing current in one coil (primary) induces an EMF in the other coil (secondary).

The induced EMF in the secondary coil is $\mathcal{E}_2 = -M \frac{dI_1}{dt}$ . Mutual inductance depends on the geometry, orientation, and core material of both coils. The coefficient of coupling $k$ relates $M$ to individual self-inductances: $M = k \sqrt{L_1 L_2}$ .

Both phenomena are crucial for understanding components like inductors and transformers.

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Key Concepts

Self-Inductance of a Solenoid

The self-inductance of a long, air-core solenoid is determined by its physical dimensions and the number of…

Induced EMF due to Self-Inductance

The induced EMF in a coil due to self-inductance is directly proportional to the rate of change of current…

Energy Stored in an Inductor

An inductor, unlike a resistor, stores energy in its magnetic field when current flows through it. This…

Self-Inductance ($L$): — Property of a coil to oppose current change in itself. Unit: Henry (H).

Induced EMF (Self): —

\mathcal{E} = -L \frac{dI}{dt}

Self-Inductance of Solenoid: —

L = \mu_0 \frac{N^2 A}{l}

(for air core)

Energy Stored in Inductor: —

U = \frac{1}{2}LI^2

Mutual Inductance ($M$): — Property of two coils where current change in one induces EMF in other. Unit: Henry (H).

Induced EMF (Mutual): —

\mathcal{E}_2 = -M \frac{dI_1}{dt}

Coefficient of Coupling ($k$): —

M = k \sqrt{L_1 L_2}

(where

0 \le k \le 1

)

Lenz's Law: — Induced EMF opposes the change in current/flux causing it.

To remember the factors affecting self-inductance of a solenoid: 'N.A.L.I.M.A.'

N — Number of turns (

N^2

)

A — Area of cross-section (

A

)

L — Length of the solenoid (

1/l

)

I — *Independent* of Current (This is the trick! Current *causes* flux, but

L

is the ratio, not dependent on

I

)

M — Material of the core (

\mu

)

A — (Just to complete the name, no specific factor)

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