1. Concept Overview
Self-induction is the process in which a changing current in a coil induces an emf in the same coil. This happens because a current-carrying coil produces its own magnetic field, and when the current changes, the magnetic flux linked with the coil also changes. According to Faraday’s law, this change in flux induces an emf.
The important point I always keep in mind: a coil resists any change in the current flowing through it. This opposition comes in the form of induced emf.
1.1. One-line idea
Changing current in a coil → changing flux → induced emf in the same coil.
2. Why Self-Induction Happens
Whenever current flows through a coil, it produces a magnetic field around it. If the current changes, the magnetic field also changes. This changing field links with the turns of the coil and produces an induced emf according to Faraday’s law.
2.1. Opposition to change (Lenz’s point of view)
According to Lenz’s law, the induced emf in the coil always opposes the change in current. This is why a coil behaves like it has inertia for electric current — it doesn’t like sudden changes.
3. Induced EMF in Self-Induction
The induced emf is produced only when the current is changing. If the current is steady and unchanging, there is no induced emf.
The mathematical form of induced emf due to self-induction is:
\( \varepsilon = -L \dfrac{dI}{dt} \)
3.1. Meaning of symbols
- \( \varepsilon \): induced emf in the same coil
- \( L \): self-inductance of the coil
- \( dI/dt \): rate of change of current
- Negative sign: indicates opposition to change (Lenz’s law)
3.2. Important note
A larger rate of change of current produces a larger induced emf. Also, a coil with more turns or a strong magnetic core has a larger self-inductance and therefore generates a stronger induced emf for the same change in current.
4. Understanding Self-Inductance
Self-inductance is the property of a coil by which it opposes any change in the current flowing through it. I think of it as the electrical equivalent of inertia — just like a body resists change in motion, a coil resists change in current.
4.1. Definition in simple words
Self-inductance (L) is the induced emf per unit rate of change of current. Mathematically:
\( L = \dfrac{\Phi_B}{I} \)
or for induced emf:
\( \varepsilon = -L \dfrac{dI}{dt} \)
4.2. Factors affecting the value of L
- Number of turns in the coil
- Coil shape and dimension
- Presence of magnetic core (iron core increases L)
- Permeability of the material inside the coil
5. Energy Viewpoint
As the current increases, work has to be done against the induced emf. This work is stored as magnetic energy. When the current decreases, the coil releases this stored energy.
5.1. Energy stored in an inductor
The magnetic energy stored in the coil is given by:
\( U = \dfrac{1}{2} L I^2 \)
This expression helps me understand why inductors are used in circuits to smooth current changes.
6. Examples That Show Self-Induction Clearly
Certain everyday situations help me visualise how self-induction works.
6.1. Sudden switching of a circuit
When a switch is turned on suddenly, the current doesn’t rise instantly due to self-induction. The coil resists the sudden increase by producing an opposing emf.
6.2. Spark in a switch
When a circuit containing a coil is opened suddenly, the current tries to drop to zero. The coil resists this drop and produces a high induced emf, which may cause a spark across the switch.
6.3. Choke in fluorescent lamps
A choke (inductor) limits the sudden rise of current when starting the lamp. Its self-inductance helps control current flow smoothly.