---
title: "Mutual Inductance — AP Physics 2 Definition & Exam Guide"
description: "Mutual inductance (M) measures how a changing current in one coil induces an emf in a nearby coil. Learn how it connects to Faraday's law in AP Physics 2 Unit 12."
canonical: "https://fiveable.me/ap-physics-2-revised/key-terms/mutual-inductance"
type: "key-term"
subject: "AP Physics 2"
unit: "Unit 12"
---

# Mutual Inductance — AP Physics 2 Definition & Exam Guide

## Definition

Mutual inductance is the phenomenon where a changing current in one coil creates a changing magnetic flux through a nearby coil, inducing an emf in it. The coefficient M quantifies the coupling, so the induced emf equals M times the rate of change of current (emf = M·dI/dt).

## What It Is

Mutual inductance is [Faraday's law](/ap-physics-2-revised/unit-12/4-electromagnetic-induction-and-faradays-law/study-guide/UqgM4DyzPPfjroi3 "fv-autolink") happening between two circuits instead of one. Coil 1 carries a current, and that current creates a magnetic field. Some of that field passes through coil 2, giving coil 2 a [magnetic flux](/ap-physics-2-revised/key-terms/magnetic-flux "fv-autolink") (Φ = BA cos θ, per the essential knowledge in Topic 12.4). If the current in coil 1 changes, the field changes, the flux through coil 2 changes, and Faraday's law says coil 2 gets an induced emf. The two coils never touch. The connection is entirely through the magnetic field.

The mutual inductance coefficient M packages all the geometry (loop sizes, separation, orientation, number of turns) into one number. It tells you how much flux coil 2 picks up per amp of current in coil 1. That makes the induced emf simple to write as emf = M·(dI/dt). A bigger M means the coils are more tightly coupled, so the same rate of current change produces a bigger induced emf. Importantly, M is symmetric. Coil 1's effect on coil 2 equals coil 2's effect on coil 1, which is why it's called *mutual*.

## Why It Matters

Mutual inductance lives in Topic 12.4 (Electromagnetic Induction and Faraday's Law) in [Unit 12](/ap-physics-2-revised/unit-12 "fv-autolink"): Magnetism and Electromagnetism. It directly supports learning objective 12.4.A, which asks you to describe the induced electric potential difference resulting from a change in magnetic flux. Mutual inductance is the two-coil version of that objective. It forces you to chain the full causal logic the exam loves to test. Changing current produces a changing field, which produces a changing flux through a second loop, which produces an [induced emf](/ap-physics-2-revised/key-terms/induced-emf "fv-autolink"). If you can walk through that chain cleanly, you've mastered the core idea of electromagnetic induction. It's also the physics behind transformers and wireless charging, which makes it a natural setup for real-world exam scenarios.

## Connections

### Faraday's law and induced emf (Unit 12)

Mutual inductance is not a separate law. It's Faraday's law applied to a second loop. The emf in coil 2 exists only because the flux through it is changing, and M·dI/dt is just a convenient repackaging of dΦ/dt.

### Magnetic flux, ΦB = BA cos θ (Unit 12)

M depends entirely on how much of coil 1's field threads coil 2. Coaxial, closely spaced loops share lots of flux and have a large M. [Perpendicular](/ap-physics-2-revised/unit-12/2-magnetism-and-moving-charges/study-guide/EquvYgnfwi2ptpX5 "fv-autolink") or far-apart loops share almost none, so M is small.

### Induced current and Lenz's law (Unit 12)

If the second coil is part of a closed circuit, the induced emf drives an [induced current](/ap-physics-2-revised/key-terms/induced-current "fv-autolink"). Lenz's law gives its direction. The induced current's own magnetic field opposes the change in flux that created it.

### Magnetic fields of current-carrying loops (Unit 12)

To actually compute M, you need the field a [current](/ap-physics-2-revised/unit-11/1-electric-current/study-guide/QaFR8etPqRmh5pdg "fv-autolink") loop produces, then find the flux it sends through the second loop. The geometry problems on the exam (concentric loops, coaxial loops) lean on this earlier Unit 12 skill.

## On the AP Exam

Mutual inductance shows up mostly in multiple-choice and quantitative problems built around two-loop geometries. A classic setup gives you two concentric circular loops in the same plane, with the inner loop's current changing at dI/dt, and asks for the magnitude of the induced emf in the outer loop. Another standard version uses two coaxial loops separated by a distance d much larger than either radius and asks you to find M itself. In both cases the move is the same. Find the flux coil 1's field puts through coil 2, identify M as flux per unit current, then multiply by dI/dt for the emf. No released FRQ has used the term verbatim, but FRQs regularly ask you to explain induced emf from changing flux, and a two-coil scenario is a natural way to frame that under LO 12.4.A. Always be ready to justify your answer with the flux-change chain, not just the formula.

## Mutual inductance vs Self-inductance

Both describe induction from a changing current, but the target is different. Self-inductance (L) is a coil inducing an emf in itself because its own changing current changes its own flux. Mutual inductance (M) is a coil inducing an emf in a different, separate coil. Quick check: one coil means self, two coils means mutual.

## Key Takeaways

- Mutual inductance means a changing current in one coil induces an emf in a nearby coil through their shared magnetic flux, with no physical contact needed.
- The induced emf in the second coil equals M times the rate of change of current in the first coil (emf = M·dI/dt).
- M depends only on geometry, including loop sizes, separation, orientation, and number of turns, not on the current itself.
- A steady current induces nothing. Only a changing current produces a changing flux, and only changing flux induces an emf, exactly as Faraday's law requires.
- M is symmetric, so coil 1's coupling to coil 2 is the same as coil 2's coupling to coil 1.
- To solve exam problems, find the flux that coil 1's field sends through coil 2, then apply Faraday's law to that changing flux.

## FAQs

### What is mutual inductance in AP Physics 2?

It's the phenomenon where a changing current in one coil induces an emf in a nearby coil, because the first coil's changing [magnetic field](/ap-physics-2-revised/unit-12/1-magnetic-fields/study-guide/8CQ1URzqZQqRb7qQ "fv-autolink") changes the flux through the second. The coefficient M quantifies it, so the induced emf is M·dI/dt. It falls under Topic 12.4, Electromagnetic Induction and Faraday's Law.

### Does mutual inductance happen when the current is constant?

No. A constant current makes a constant magnetic field and constant flux through the second coil, and constant flux induces zero emf. Only a changing current (dI/dt ≠ 0) induces an emf in the neighboring coil.

### What's the difference between mutual inductance and self-inductance?

Self-inductance is a coil inducing an emf in itself from its own changing current, while mutual inductance is one coil inducing an emf in a different coil. Same Faraday's law physics, different target. Count the coils: one is self, two is mutual.

### How do you find mutual inductance between two loops?

Calculate the magnetic flux that loop 1's current sends through loop 2, then divide by the current. M = Φ₂/I₁. In exam problems with coaxial loops far apart (d much larger than the radii), you approximate loop 1's field at loop 2 as roughly uniform over the small loop's area.

### Is mutual inductance on the AP Physics 2 exam?

Yes, it falls under Unit 12 and learning objective 12.4.A, which covers induced potential difference from changing magnetic flux. Expect multiple-choice questions with two-loop geometries, like concentric coplanar loops or coaxial loops, asking for M or the induced emf.

## Related Study Guides

- [12.4 Electromagnetic Induction and Faraday's Law](/ap-physics-2-revised/unit-12/4-electromagnetic-induction-and-faradays-law/study-guide/UqgM4DyzPPfjroi3)

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