---
title: "Induced EMF — AP Physics 2 Definition & Exam Guide"
description: "Induced emf is the voltage created by a changing magnetic flux (Faraday's law). Learn how it drives induced current and shows up on AP Physics 2 FRQs."
canonical: "https://fiveable.me/ap-physics-2-revised/key-terms/induced-emf"
type: "key-term"
subject: "AP Physics 2"
unit: "Unit 12"
---

# Induced EMF — AP Physics 2 Definition & Exam Guide

## Definition

Induced emf is the electric potential difference produced in a conductor or loop when the magnetic flux through it changes, given by Faraday's law (ε = -ΔΦB/Δt); its direction opposes the flux change (Lenz's law), and on AP Physics 2 it lives in Topic 12.4.

## What It Is

Induced emf is the [voltage](/ap-physics-2-revised/key-terms/voltage "fv-autolink") that appears in a loop or [conductor](/ap-physics-2-revised/unit-11/3-resistance-resistivity-and-ohms-law/study-guide/y0ZmKqhOPqeLWZFa "fv-autolink") whenever the magnetic flux through it changes. Flux is ΦB = BA cos θ, so you can change it three ways. Change the field strength B, change the area A, or change the angle θ between the field and the area vector. Any of those changes induces an emf equal to the rate of flux change, ε = -ΔΦB/Δt (multiply by N for a coil with N turns). That's Faraday's law, and it's the heart of Topic 12.4.

The negative sign is Lenz's law. The induced emf always points in the direction that opposes the change in flux. Think of the loop as stubborn. If flux is increasing, the induced current makes a [magnetic field](/ap-physics-2-revised/unit-12/1-magnetic-fields/study-guide/8CQ1URzqZQqRb7qQ "fv-autolink") fighting that increase; if flux is decreasing, the induced current tries to prop it back up. This is really conservation of energy in disguise, because if the loop helped the change instead, you'd get a runaway free-energy machine.

## Why It Matters

Induced emf is the payoff concept of [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](/ap-physics-2-revised/key-terms/magnetic-flux "fv-autolink"). Everything earlier in the unit (magnetic fields, forces on moving charges, flux) builds toward this. It's also where magnetism reconnects with circuits, because an induced emf can drive a current through resistors just like a battery can. Generators, transformers, and the classic sliding-rod-on-rails problem all run on this one idea, which is why it's one of the most heavily tested concepts in the unit.

## Connections

### [Induced current (Unit 12)](/ap-physics-2-revised/key-terms/induced-current)

Induced emf is the cause; [induced current](/ap-physics-2-revised/key-terms/induced-current "fv-autolink") is the effect. Once Faraday's law gives you the emf, the loop acts like a battery and Ohm's law gives the current, I = ε/R. The emf exists even if the loop is broken and no current flows.

### Magnetic flux and Faraday's law, Topic 12.4 (Unit 12)

You can't compute an induced emf without first computing flux, ΦB = BA cos θ. Most exam problems are really flux bookkeeping. Figure out which of B, A, or θ is changing, find the rate, and the emf falls out.

### Circuits and Ohm's law (Unit 11)

An induced emf behaves exactly like a battery's emf in a circuit. In the sliding-rod problem, the rod is a moving battery with ε = BLv, and from there it's a standard [Unit 11](/ap-physics-2-revised/unit-11 "fv-autolink") circuit with current, resistance, and power dissipation.

### [Mutual inductance (Unit 12)](/ap-physics-2-revised/key-terms/mutual-inductance)

When a changing current in one coil induces an emf in a neighboring coil, that's [mutual inductance](/ap-physics-2-revised/key-terms/mutual-inductance "fv-autolink"), which is induced emf happening between two circuits instead of within one. It's the physics behind transformers.

## On the AP Exam

Multiple-choice questions love giving you a flux-change scenario and asking for the average induced emf. Common setups include a loop rotating 90° in a field (the θ in BA cos θ changes), a rod sliding on rails at constant velocity (use ε = BLv, then I = BLv/R), a rotating rod touching a conducting rim (ε = ½BωL²), and a solenoid whose current decays exponentially, where you have to differentiate or use ΔΦ/Δt. The 2021 long FRQ built an entire problem around an electromagnet's field changing with current, requiring you to connect a B-versus-I graph to the flux through a loop and the resulting emf. Expect to do three things. Identify what's changing in ΦB = BA cos θ, apply ε = -NΔΦB/Δt to get magnitude, and use Lenz's law to justify direction in words. Direction reasoning is where points get lost, so always state which way flux is changing and why the induced current opposes it.

## induced emf vs Induced current

Induced emf is a voltage; induced current is the charge flow that voltage can drive. A changing flux always induces an emf in a loop, but you only get an induced current if the loop is a closed conducting path, and its size depends on resistance (I = ε/R). On FRQs, calculate the emf first, then find the current. If a question says the loop is open or made of an insulator, there's still an emf but no current.

## Key Takeaways

- Induced emf is the potential difference created by a changing magnetic flux, given by Faraday's law: ε = -NΔΦB/Δt.
- Flux can change three ways, through a changing field strength B, a changing area A, or a changing angle θ, and any one of them induces an emf.
- Lenz's law (the minus sign) means the induced emf drives current in the direction that opposes the change in flux, which is conservation of energy at work.
- A constant magnetic field through a stationary loop induces nothing; only a changing flux induces an emf.
- An induced emf exists even in an open loop, but induced current only flows if the circuit is closed, with I = ε/R.
- For a rod sliding on rails perpendicular to a field, the motional emf is ε = BLv, and the rod acts like a battery in the circuit.

## FAQs

### What is induced emf in AP Physics 2?

It's the voltage produced in a conductor or loop when the magnetic flux through it changes, calculated with Faraday's law, ε = -NΔΦB/Δt. It's the central idea of Topic 12.4 in Unit 12.

### Does a magnetic field by itself induce an emf?

No. A steady field through a stationary loop induces nothing. Only a change in flux, meaning a change in B, the area, or the angle between them, produces an induced emf.

### What's the difference between induced emf and induced current?

Induced emf is the voltage from the changing flux; induced current is what flows if the circuit is closed, with I = ε/R. You can have an emf with zero current if the loop is open or non-conducting.

### Why is there a negative sign in Faraday's law?

The negative sign is Lenz's law. It tells you the induced emf opposes the change in flux, so an increasing flux induces a current whose own field fights the increase. Without this opposition, energy wouldn't be conserved.

### How do I find induced emf when a loop rotates in a magnetic field?

The angle θ in ΦB = BA cos θ changes, so find the flux before and after, then use average emf = NΔΦB/Δt. For a loop rotating 90° from perpendicular, the flux goes from BA to zero, so the average emf is BA/t.

## 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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