1. Concept Overview
Mutual induction is the process by which a changing current in one coil induces an emf in a nearby coil. This happens because the first coil creates a magnetic field, and when the current in that coil changes, the magnetic flux linked with the second coil also changes. According to Faraday’s law, this change in flux induces an emf in the second coil.
I think of mutual induction as a kind of electrical “communication” between coils — one coil affects the other without any direct electrical connection.
1.1. Simple one-line idea
Changing current in coil 1 → changing flux → induced emf in coil 2.
2. Why Mutual Induction Happens
Whenever current flows in a coil, it produces a magnetic field around it. If a second coil is placed close enough, this magnetic field links with it. So when the current in the first coil changes, the magnetic flux through the second coil changes, leading to an induced emf in the second coil.
2.1. Link with Faraday’s law
Faraday’s law states that any change in magnetic flux induces an emf. In mutual induction, the flux of one coil is controlled by the current in the other coil, so changing current produces changing flux in the neighbouring coil.
3. Induced EMF in Mutual Induction
The induced emf in the second coil depends on how quickly the current in the first coil changes. The relationship is:
\( \varepsilon_2 = -M \dfrac{dI_1}{dt} \)
3.1. Meaning of each term
- \( \varepsilon_2 \): emf induced in the second coil
- \( M \): coefficient of mutual induction
- \( dI_1/dt \): rate of change of current in the first coil
- Negative sign: shows opposition (Lenz’s law)
3.2. What determines the magnitude
If the current in coil 1 changes rapidly, a larger emf appears in coil 2. A slow change in current produces a smaller emf.
4. Coefficient of Mutual Induction
The coefficient of mutual induction \( M \) measures how strongly two coils influence each other through changing magnetic flux. A higher value of \( M \) means a larger induced emf for the same rate of change of current in coil 1.
4.1. Definition
Coefficient of mutual induction is the induced emf in one coil per unit rate of change of current in the other coil.
Mathematically:
\( M = \dfrac{\varepsilon_2}{\dfrac{dI_1}{dt}} \)
4.2. Factors that affect M
- Number of turns in each coil
- Area of the coils
- Distance between the coils
- Orientation of the coils
- Material between them (iron core increases M)
5. Understanding Mutual Flux Linkage
To visualise mutual induction, I imagine coil 1 producing a magnetic field. Some of the field lines pass through coil 2. These shared lines represent the mutual flux. When coil 1’s current changes, the number of lines linking coil 2 changes, producing an induced emf.
5.1. Ideal vs. real situations
In an ideal case, all magnetic flux of coil 1 passes through coil 2, giving maximum mutual induction. In real coils, only part of the flux links with the second coil, so the induced emf is smaller.
6. Lenz’s Law and Mutual Induction
The direction of induced emf in coil 2 follows Lenz’s law. It always opposes the change in flux caused by coil 1. This ensures energy conservation and prevents the induction process from amplifying itself endlessly.
6.1. Opposition explained
If the current in coil 1 increases, coil 2 tries to oppose the increase by producing a magnetic field in the opposite direction. If the current in coil 1 decreases, coil 2 tries to oppose the decrease by producing a field in the same direction.
7. Visualising a Common Setup
A simple setup often used to demonstrate mutual induction includes two coils — a primary coil connected to a battery or AC source, and a secondary coil connected to a galvanometer.
7.1. What happens during switching
- When the primary circuit is switched on, current rises → flux rises → induced emf in secondary.
- When the primary is steady, no change in flux → no emf in secondary.
- When the primary is switched off, current falls → flux falls → induced emf again in the secondary but in the opposite direction.
8. Applications of Mutual Induction
Many important electrical devices rely on mutual induction because it allows energy to be transferred from one coil to another without direct contact.
8.1. Transformers
Transformers work purely on mutual induction. The alternating current in the primary coil continuously changes the flux and induces emf in the secondary coil.
8.2. Induction coils
Used for generating very high voltages. Rapidly changing current in the primary induces a large emf in the secondary due to a high number of turns.
8.3. Wireless charging systems
Changing current in the charging pad coil induces current in the device coil, transferring energy wirelessly.