Short Answer

Mutual induction is the phenomenon in which a changing current in one coil induces an electromotive force (EMF) in a nearby coil. This happens because the changing current produces a changing magnetic field, which links with the second coil and induces a voltage in it.

Mutual induction is the basic working principle of transformers, generators, and many communication systems. The amount of induced EMF depends on how quickly the current changes and how closely the coils are placed.

Detailed Explanation

Mutual induction

Mutual induction is an important concept in electromagnetism that explains how two coils placed close to each other can interact through magnetic fields. When an electric current flows through a coil, it produces a magnetic field around it. If this current changes, the magnetic field also changes. When another coil is placed near this changing magnetic field, an EMF is induced in the second coil. This effect is called mutual induction.

Mutual induction was discovered by Michael Faraday and Joseph Henry independently. It forms the basis of transformers, wireless chargers, generators, induction coils, and many other electrical devices. Whenever energy is transferred from one coil to another without direct electrical contact, mutual induction is involved.

Definition of mutual induction

Mutual induction is defined as:
The process by which a changing current in one coil induces an EMF in another nearby coil due to the changing magnetic flux.

The coil in which current changes is called the primary coil, and the coil in which EMF is induced is called the secondary coil.

How mutual induction works

Consider two coils kept near each other:

• Coil A (primary coil) is connected to a battery and switch.
• Coil B (secondary coil) is connected to a galvanometer.

When the switch is closed:

1. Current begins to increase in the primary coil.
2. This produces a changing magnetic field around the coil.
3. The magnetic field links with the nearby secondary coil.
4. Because the flux through the secondary coil changes, an EMF is induced in it.
5. The galvanometer shows a momentary deflection.

When the switch is opened:

• Current in the primary coil decreases.
• Magnetic flux decreases.
• A new EMF is induced in the secondary coil, but in the opposite direction.

This is the essence of mutual induction—a change in current in one coil creates a voltage in another.

Mathematical expression of mutual induction

The induced EMF in the secondary coil is given by:

E = – M (dI/dt)

Where:

• E = induced EMF in the secondary coil
• M = mutual inductance
• dI/dt = rate of change of current in the primary coil
• Negative sign indicates direction opposing the change

Mutual inductance M depends on:

• Number of turns of both coils
• Distance between the coils
• Area of the coils
• Permeability of the core material

Mutual inductance is measured in Henry (H).

Factors affecting mutual induction

1. Number of turns in the coils
   More turns → greater induced EMF.
2. Distance between coils
   Smaller distance → stronger interaction.
3. Area of the coils
   Larger area → more magnetic flux linkage.
4. Core material
   Soft iron cores increase mutual induction by increasing magnetic flux.
5. Orientation of coils
   Coils placed parallel and close are more effective.

Practical examples of mutual induction

1. Transformers

Transformers work completely on mutual induction.

• Primary coil receives AC.
• Changing current produces changing flux.
• This flux induces EMF in secondary coil.

Depending on the number of turns, it becomes step-up or step-down.

2. Generator coils

In generators, rotating coils produce changing magnetic flux. This changing flux induces EMF in another set of coils through mutual induction.

3. Wireless charging

Mobile phones and electric toothbrushes use coils for wireless charging.
A coil in the charger produces a changing magnetic field, inducing EMF in the coil of the device.

4. Induction coils

Used in laboratories to generate high voltage. Based on rapid changes in current in the primary coil.

5. Telephone and communication systems

Old telephones used induction between coils to transmit voice signals.

Difference between mutual induction and self-induction

• Self-induction happens within the same coil.
• Mutual induction happens between two different coils.

Self-induction opposes changes in its own current, while mutual induction transfers energy to another coil.

Importance of mutual induction

Mutual induction is essential because it:

• Enables voltage transformation in transformers
• Helps generate electricity in power stations
• Makes wireless charging possible
• Enables induction heating
• Forms the basis of communication devices
• Allows efficient transfer of electrical energy without direct connection

Without mutual induction, modern electrical systems and power distribution would not function.

Conclusion

Mutual induction is the phenomenon in which a changing current in one coil induces an EMF in another nearby coil due to changing magnetic flux. It plays a central role in the working of transformers, generators, wireless chargers, and many other devices. Mutual induction allows the transfer of electrical energy from one circuit to another without any physical connection, making it one of the most important concepts in electromagnetism.