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).
Mutual inductance is Faraday's law 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 (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.
Mutual inductance lives in Topic 12.4 (Electromagnetic Induction and Faraday's Law) in Unit 12: 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. 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.
Keep studying AP® Physics 2 Unit 12
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 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. 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 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.
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.
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.
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.
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 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.
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.
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.
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.
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.
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