1. Self-Induction
Consider a coil through which an electric current is flowing. Due to this current, a magnetic field is produced that links with the coil itself. If for any reason the current changes, the magnetic flux also changes, inducing an electromotive force (emf) in the coil. This phenomenon is known as self-induction.
In accordance with Lenz's law, this induced emf opposes the change in current and is therefore known as a back emf ($\mathcal{E}_L$). The back emf is directly proportional to the rate of change of current:
$\mathcal{E}_L \propto \frac{\Delta I}{\Delta t} \implies \mathcal{E}_L = -L \frac{\Delta I}{\Delta t}$
Where $L$ is the self-inductance of the coil.
Self-Inductance (Definition & Formula)
"Self-inductance is defined as the ratio of the back emf induced in a coil to the rate of change of current through itself."
$L = \frac{\mathcal{E}_L}{\frac{\Delta I}{\Delta t}}$
Factors affecting Self-Inductance: Dimensions of the coil, number of turns, and magnetic permeability of the core material.
2. Mutual Induction
Figure: Primary and secondary coils illustrating mutual induction and magnetic flux linkage.
Consider two coils placed close to each other. The coil connected to a source of emf is called the primary coil, and the other connected to a galvanometer is called the secondary coil. Magnetic flux produced by the current in the primary links with the secondary coil. When the primary current changes, an emf is induced in the secondary coil. This phenomenon is called mutual induction.
The back emf ($\mathcal{E}_s$) induced in the secondary coil is directly proportional to the 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 $M$ is the mutual inductance between the two coils.
Mutual Inductance (Definition & Formula)
"Mutual inductance is defined as the ratio of the back emf induced in the secondary coil to the rate of change of current through the primary coil."
$M = \frac{\mathcal{E}_s}{\frac{\Delta I_p}{\Delta t}}$
Factors affecting Mutual Inductance: Number of turns in both coils, their cross-sectional area, their closeness (coupling), and the core material.
SI Unit: The Henry
The SI unit of both self-inductance and mutual inductance is the Henry (H).
Definition of 1 Henry
"The self-inductance (or mutual inductance) of a coil is 1 Henry if a current varying through it (or the primary coil) at the rate of 1 ampere per second induces a back emf of 1 volt."
$1 \, \text{H} = \frac{1 \, \text{V}}{1 \, \text{A/s}} = 1 \, \text{V} \cdot \text{s} \cdot \text{A}^{-1}$
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