Short Answer:

Mutual induction is the process by which a changing current in one coil produces an electromotive force (EMF) in a nearby coil. This happens because the changing magnetic field created by the first coil cuts through the second coil and induces voltage in it. It is the basic principle used in transformers and many wireless energy transfer systems.

In mutual induction, no physical connection is needed between the coils—only magnetic coupling. The strength of mutual induction depends on the number of turns in the coils, their distance, orientation, and how rapidly the current changes in the first coil.

Detailed Explanation:

Mutual induction

Mutual induction is an important concept in electromagnetism and electrical engineering. It refers to the phenomenon where a changing current in one coil induces a voltage (EMF) in another nearby coil through the magnetic field it creates. The two coils are usually called the primary coil (which carries the changing current) and the secondary coil (where EMF is induced).

This process is entirely based on Faraday’s Law of Electromagnetic Induction, which says that a changing magnetic flux through a coil will induce an EMF. In mutual induction, the magnetic field generated by the primary coil links with the secondary coil and causes a change in magnetic flux, thereby inducing EMF.

How mutual induction works

When an alternating current (AC) flows through the primary coil, it produces a changing magnetic field around it. If the secondary coil is placed close enough to the primary coil, this changing magnetic field passes through the turns of the secondary coil.

According to Faraday’s Law, this changing magnetic field causes a change in magnetic flux in the secondary coil, which results in an induced voltage or EMF. This voltage can cause current to flow if the secondary coil is connected to a closed circuit.

Mathematical expression

The EMF (ε\varepsilonε) induced in the secondary coil due to mutual induction is given by:

ε=−M⋅dIdt\varepsilon = -M \cdot \frac{dI}{dt}ε=−M⋅dtdI​

Where:

• ε\varepsilonε = induced EMF in the secondary coil
• MMM = mutual inductance between the coils (measured in henries, H)
• dIdt\frac{dI}{dt}dtdI​ = rate of change of current in the primary coil
• The negative sign follows Lenz’s Law, showing that the induced EMF opposes the change in current

Factors affecting mutual induction

1. Number of turns: More turns in either coil increases the induced EMF.
2. Distance between coils: Closer coils have stronger mutual coupling.
3. Core material: Using iron or other magnetic materials increases the magnetic linkage.
4. Orientation: Coils aligned properly to maximize magnetic flux linkage give better results.

Applications of mutual induction

• Transformers: Step-up and step-down voltages in power systems.
• Wireless charging: Inductive charging systems for phones and vehicles.
• Induction cookers: Generate heat using magnetic coupling.
• Electric generators: Use mutual induction to generate electricity.
• Inductive sensors: Detect metallic objects and motion.

Real-life example

In a transformer, AC current in the primary coil creates a changing magnetic field in the core. This magnetic field links with the secondary coil and induces voltage, allowing power to be transferred without any direct connection between the coils.

Conclusion:

Mutual induction is the process by which a changing current in one coil induces an EMF in another nearby coil through a magnetic field. It forms the working principle of many important electrical devices like transformers and wireless chargers. The efficiency of mutual induction depends on coil design, material, and magnetic linkage, making it a vital concept in modern electrical engineering.