Self – Induction

Self-induction is the phenomenon where a changing current in a coil induces an EMF in the same coil, opposing the change that caused it. Think of it as the "electrical inertia" of a circuit — it resists sudden changes in current, just as mechanical inertia resists sudden changes in motion.

The phenomenon of electromagnetic induction in which a change in current through a coil induces an EMF in the same coil, opposing the change in current, is called self-induction.

The self-inductance of a coil is defined as the ratio of the total magnetic flux linkage to the current flowing through it.

NΦ_B ​= LI

Where:

• N = number of turns
• Φ_B​ = magnetic flux linked per turn
• I = current flowing through the coil
• L = coefficient of self-inductance (self-inductance)

• When current in a coil increases → flux linked with coil increases → induced EMF opposes the increase (opposes growth of current).
• When current in a coil decreases → flux linked with the coil decreases → induced EMF opposes the decrease (opposes decay of current).
• This opposing behaviour is a direct consequence of Lenz's Law — the induced EMF always opposes the cause producing it.

The induced EMF due to self-induction is given by:

Step-by-Step Derivation

1. Flux linkage of coil: NΦB = LI
2. By Faraday's Law: ε = −\[\frac {d(NΦ_B)}{dt}\]
3. Substituting: ε = −\[\frac {d(LI)}{dt}\]
4. Since L is constant for a given coil geometry: ε = −L\[\frac {dI}{dt}\]

Negative sign significance: Indicates that the induced EMF always opposes the change in current (direction, not magnitude).

• 1 Henry: A coil has a self-inductance of 1 henry if a current change of 1 A/s induces an EMF of 1 volt in it.
• Dimensional Formula: [ML²T⁻²A⁻²]

• Self-inductance depends only on the geometry of the coil (number of turns, area, length, core material) — not on the current or EMF.
• An ideal, infinitely thin straight wire has zero self-inductance because it encloses no appreciable flux.
• An ideal inductor has zero resistance and only opposes change in current, never steady current.
• Inductors do not oppose current itself — they oppose only the rate of change of current.
• Self-inductance is analogous to inertia in mechanics — it represents electrical "resistance to change."

Problem: A coil of 200 turns and self-inductance 20 mH carries a current of 4 mA. Find the magnetic flux linked per turn.

Solution:

Given: N = 200, L = 20 mH = 20 × 10^-3 H, I = 4 mA = 4 × 10^-3 A

Using NΦ_B = LI:

Answer: Flux per turn = 4 × 10⁻⁷ Wb

Imagine a loaded truck moving at constant speed. To suddenly speed it up or stop it requires extra force because of its inertia. Similarly, an inductor "resists" a sudden change in current — it needs extra EMF (energy) to change the current quickly. This is why self-inductance is often called electrical inertia.

Everyday Applications:

• Chokes/ballasts in tube lights and fluorescent lamps
• Inductors in filter circuits (radios, power supplies)
• Ignition coils in vehicles (sudden current interruption produces high voltage spark)