What Is Mutual Inductance: Meaning, Formula & Practical Applications

Key Takeaways
 

• Mutual inductance, in simple terms, can be understood as wireless energy transfer.
   
• We can see mutual inductance in our everyday devices.
   
• Mutual inductance is a great example of how magnets and electricity work together.

Mutual inductance is the ability of one coil to create a voltage in another coil when the magnetic field around it changes. It happens when the coils are close, and the magnetic field from one links with the other.

Think of a mobile phone charger. Inside, a transformer has two coils. When electricity flows through the first coil, it creates a magnetic field. This field links to the second coil and produces voltage. That voltage then charges your phone. The two coils do not touch, but energy still moves from one to the other. This is mutual inductance.

Phone Charger Example

Mutual inductance makes wireless charging, transformers, and many electric devices possible by transferring energy through magnetism.

In this blog, we will see the real concept of mutual inductance with its real-life applications.

Understanding Mutual Inductance in Simple Terms

When electric current flows through a coil, it creates a magnetic field around it. If there is another coil nearby, this magnetic field can pass through it too. If the current in the first coil changes, the magnetic field also changes. This changing field creates a voltage (called induced emf) in the second coil. This effect is known as mutual inductance.

How Does It Work?

Let’s say coil 1 has N₁ turns and coil 2 has N₂ turns. When current I₁ flows through coil 1, it creates a magnetic field B. Some of this field passes through coil 2, especially when the coils are close.

If we change I₁ with time, then the magnetic flux in coil 2 also changes. This causes an emf (voltage) to be induced in coil 2, as per Faraday’s Law:

ε=-dϕ​/dt

So,

ε₂₁​=-N₂dϕ₂₁/dt
 

The voltage in coil 2 depends directly on how fast we change the current in coil 1. We call this effect mutual inductance, and we represent it as:

N₂​ϕ₂₁=M₂₁​I₁

Where M₁₂ or M₂₁ is the mutual inductance.
It has a unit called henry (H).

What Happens the Other Way Around?

If the current I₂ flows in coil 2 and we change it with time, it also creates an emf in coil 1. The process works in both directions:

ε₁₂=-N₁​dϕ₁₂/dt

N₁​ϕ₁₂=M₁₂​I₂
 

This shows that mutual inductance is a shared property between the two coils. Both coils can induce voltage in each other when their currents change with time.
 

Bonus tip:-While often positive, mutual inductance can be engineered to be negative by reversing the coil orientation or winding direction

What Is the Reciprocity Theorem in Mutual Inductance?

The reciprocity theorem tells us that the mutual inductance between two coils works the same in both directions.

In simple terms, if coil 1 creates a changing current and induces a voltage in coil 2, then coil 2 will create the same effect in coil 1 if the current is changed in coil 2. The value of mutual inductance remains the same either way.

This happens when there is no special material (like iron) between the coils, just air or vacuum.

Mathematically:
 

M₁₂=M₂₁
 

So, we just write:
 

M=Mutual Inductance between the two coils
 

This idea comes from Ampere’s law and Biot–Savart’s law, which explain how magnetic fields behave around electric currents.

EMF of Mutual Inductance

When the electric current in one coil changes, it creates a changing magnetic field. If there is another coil nearby, this changing field passes through it and produces a voltage. This voltage is called the emf of mutual inductance.

We write it as:

ε=−M (dI/dt)

Where:
 

• ε (emf) is the voltage produced in the second coil
   
• M is the mutual inductance between the two coils
   
• dI/dt is how fast the current in the first coil is changing with time
   
• The minus sign shows that the induced emf works in the opposite direction to the change (as per Lenz's Law)
   

If the current in one coil changes quickly, it creates a stronger voltage in the other coil. The coils do not touch, but the energy still transfers. This is how transformers, wireless chargers, and induction cookers work.

How to Find Mutual Inductance?

To find mutual inductance, we measure how much voltage (emf) is induced in one coil when the current in the other coil changes over time. Mutual inductance shows how strongly two coils affect each other through their magnetic fields.

We use this formula:

M=ε/dI/dt

Where:
 

• M is the mutual inductance
   
• ε is the induced emf in the second coil
   
• dI/dt is the rate at which current changes in the first coil

Simple Steps:
 

1. Pass a changing current through the first coil
    
2. Measure the emf (voltage) induced in the second coil.
    
3. Use the formula to calculate the mutual inductance.

This value is measured in henry (H). A higher value means the coils are better at transferring energy through magnetic fields.

Factors That Affect Mutual Inductance

Several things change how strongly two coils can affect each other through magnetic fields. These factors directly affect the value of mutual inductance between the coils.

1. Area of Cross-Section

If the coils have a larger cross-sectional area, more magnetic field lines can pass through the other coil. This increases mutual inductance.

2. Number of Turns in Each Coil

More turns in the coils mean stronger magnetic fields and better linking between the coils. Mutual inductance becomes higher with more turns.

3. Space Between the Coils

If the coils are close together, more magnetic field lines pass from one coil to the other. As the space increases, mutual inductance decreases.

5. Length of the Coils (for Solenoids)

In solenoids, a longer length means weaker magnetic field strength per turn, which can reduce mutual inductance if other factors remain the same.

Mutual inductance depends on both the physical design of the coils and the properties of the space or material between them. Optimising these factors improves the efficiency of electromagnetic energy transfer.

Real-Life Demonstrations of Mutual Inductance in Electromagnetism

Mutual inductance occurs when a changing current in one coil induces a voltage in another nearby coil. This is a key principle behind Faraday’s Law, and it’s widely used in everyday devices. Below are real-world examples that show mutual inductance in action.

Transformers – Power Transfer Through Magnetic Fields
 

• How it works: AC in the primary coil creates a changing magnetic field that induces voltage in the secondary coil.
   
• Key principle: Faraday’s Law – a changing magnetic field induces EMF.
   
• Used in: Electrical grids to step voltage up or down.

Inductive Charging – Wireless Battery Power
 

• How it works: A coil in the charger generates a magnetic field; the device coil receives it and charges the battery.
   
• Key principle: Mutual inductance enables energy transfer without wires.
   
• Used in: Wireless phone chargers, electric toothbrushes.

Wireless Power Transfer – Energy Without Cables
 

• How it works: Coils tuned to the same frequency exchange energy via a shared magnetic field.
   
• Key principle: Resonant inductive coupling.
   
• Used in: EV chargers, medical implants.

Electric Guitars – Converting Vibrations into Sound
 

• How it works: Metal strings disturb a magnetic field near a coil, inducing voltage.
   
• Key principle: Changing magnetic flux creates a signal (Faraday’s Law).
   
• Used in: Guitar pickups and audio equipment.
   

These examples clearly show how mutual inductance turns fundamental electromagnetic principles into practical technologies that power, charge, and amplify devices we use every day.
 

Bonus Tip:-In some sensors, changes in mutual inductance between coils are used to detect the position or movement of objects

Conclusion

Mutual inductance lets one coil affect another through magnetic fields. It helps transfer energy without direct connection and is widely used in transformers, chargers, and electronic devices. It works when the current in one coil changes and creates voltage in the other coil.

FAQ’s

1. What makes mutual inductance different from self-inductance?

Mutual inductance involves two separate coils influencing each other, whereas self-inductance occurs within a single coil, affecting its own current.

2. Can mutual inductance occur without a magnetic core?

Yes, but it's less efficient. A magnetic core, like iron, increases the magnetic coupling between the coils.

3. Why does mutual inductance work only with changing currents?

Only a changing current produces a varying magnetic field, which is necessary to induce voltage in the second coil, as stated by Faraday’s Law.

4. Does coil orientation affect mutual inductance?

Absolutely. Coils must be properly aligned closer and parallel for maximum magnetic interaction and efficient energy transfer.

5. Is mutual inductance used only in large electrical systems?

Not at all. It’s used in small everyday devices too, like wireless chargers, electric toothbrushes, and guitar pickups.

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