What is Mutual Inductance? Meaning and Formula

Physics · Electromagnetic Induction · NEET

Mutual inductance (M) tells you how strongly two nearby coils are magnetically linked: when the current in coil 1 changes, it changes the flux through coil 2 and induces an emf there. The formula is N₂Φ₂ = M I₁, so M = (flux linkage in coil 2) / (current in coil 1), measured in henry (H). Memory hook: "one coil talks, the other coil listens — M measures how loud the message is."
Mutual Inductance: coil 1 drives flux into coil 2Coil 1 (current I₁)Coil 2 (flux Φ₂, emf ε₂)magnetic flux links the two coilsM = N₂Φ₂ / I₁ (unit: henry)
A changing current I₁ in coil 1 sends magnetic flux through coil 2, inducing an emf ε₂. Mutual inductance M = N₂Φ₂ / I₁ measures this coupling; it depends only on the coils' geometry, not on I₁.

Your doubts, answered

Is mutual inductance the same as self-inductance?

No. Self-inductance is one coil reacting to its OWN changing current (flux it makes through itself). Mutual inductance is about TWO coils: a changing current in coil 1 induces an emf in a separate coil 2. Self = talking to yourself, mutual = talking to a neighbour. Both are measured in henry and both depend only on geometry, not on the current.

What do the small numbers in M21 mean?

In M₂₁ the first number (2) is the coil where flux/emf appears, and the second number (1) is the coil carrying the current. So N₂Φ₂ = M₂₁ I₁ means: current I₁ in coil 1 produces flux linkage N₂Φ₂ in coil 2. A useful NEET fact is M₁₂ = M₂₁, so the order does not change the value.

Why does M not depend on the current?

Flux is proportional to current (Φ ∝ I), so when you divide flux linkage by current, the current cancels out. What is left, M, depends only on the shape, size, number of turns, spacing of the coils, and the material between them. Change the current and both flux and emf change, but M stays fixed — just like resistance stays fixed when you change voltage.

What is the SI unit of mutual inductance?

The henry (H). From ε = M (dI/dt), one henry means an emf of 1 volt is induced in coil 2 when the current in coil 1 changes at 1 ampere per second. So 1 H = 1 V·s/A = 1 Wb/A. This is the same unit as self-inductance.

Do I always need two coils for mutual inductance?

Yes. Mutual inductance is defined between a pair of circuits — a source coil and a linked coil. If there is only one coil reacting to itself, that is self-inductance, not mutual. In NEET numericals, look for two solenoids, two loops, or a primary and secondary — that is your signal to use M.

⚠️ The NEET trap
M depends on the current I₁, so a bigger current gives a bigger mutual inductance.
M depends only on geometry and the medium (turns, area, spacing, μᵣ). Bigger current raises the flux and the emf, but M itself is unchanged.
🧠 Flux is proportional to current, so I cancels when you compute M = NΦ/I. M is a constant of the pair, like resistance is a constant of a wire.

Real NEET questions

NEET 2021

Two conducting circular loops of radii R₁ and R₂ are placed in the same plane with their centres coinciding. If R₁ ≫ R₂, the mutual inductance M between them will be directly proportional to:

A · R₁² / R₂²
B · R₂² / R₁
C · R₁ / R₂
D · R₂ / R₁
Solution: Use the definition M = Φ₂ / I₁ (flux through loop 2 per unit current in loop 1). Step 1: Take the big loop (R₁) as the source. Its magnetic field at the centre is B = μ₀I / (2R₁). Because R₁ ≫ R₂, this field is nearly uniform over the whole tiny inner loop. Step 2: Flux through the small loop = B × area = [μ₀I / (2R₁)] × πR₂² = μ₀ I π R₂² / (2R₁). Step 3: Divide by the current to get M = Φ / I = μ₀ π R₂² / (2R₁). Step 4: Keeping only the R-dependence, M ∝ R₂² / R₁. So the answer is B. Note how the current I cancels — M depends only on the sizes of the two loops.

Solved Electromagnetic Induction NEET PYQs

Try the real previous-year questions from this chapter — each with the answer and a full solution.

See all 16 Electromagnetic Induction NEET PYQs ›
Next concept: Mutual Inductance of Two Coaxial SolenoidsKeep learning — 2 minFeeling ready? Solve the Electromagnetic Induction NEET PYQs ›Or practice on your phone — get the free MedicNEET app ›

Frequently asked

What is the formula for mutual inductance?

N₂Φ₂ = M I₁, which rearranges to M = N₂Φ₂ / I₁. In words, mutual inductance equals the total flux linkage in the second coil divided by the current in the first coil. The induced emf form is ε₂ = −M (dI₁/dt).

What is the SI unit of mutual inductance?

The henry (H), where 1 H = 1 Wb/A = 1 V·s/A. It is the same unit used for self-inductance.

What factors does mutual inductance depend on?

Number of turns of both coils, their cross-sectional area, the distance and orientation between them, and the relative permeability μᵣ of the material between them. It does NOT depend on the current.

Is M₁₂ always equal to M₂₁?

Yes. For any pair of coils, M₁₂ = M₂₁ = M. This reciprocity is a standard NEET result, so you can compute M whichever way is easier.

Why is mutual inductance important for NEET?

It is the working principle of transformers and is a repeat topic in the Electromagnetic Induction chapter. Questions test the formula M = NΦ/I, the henry unit, and the fact that M depends only on geometry — exactly the traps NTA likes to set.