Electromotive force in AP Physics C: E&M

Electromotive force (emf, symbol ℰ) is the energy per unit charge a source like a battery supplies to push charge through a circuit; despite the name, it's not a force but a potential difference measured in volts, equal to terminal voltage only when no current flows or internal resistance is zero.

Verified for the 2027 AP Physics C: E&M examLast updated June 2026

What is electromotive force?

Electromotive force (emf, written ℰ) is the energy per unit charge that a source provides to move charge through a circuit. Think of a battery as a charge pump. Charges lose energy as they push through resistors, and the emf source is what lifts them back up so current keeps flowing. The units are joules per coulomb, which means emf is measured in volts, exactly like potential difference.

The name is misleading. Emf is not a force at all. It's a leftover term from old physics that stuck around. What it really describes is how much work per coulomb a source does on charge carriers. A 9 V battery has an emf of 9 V because it does 9 joules of work on every coulomb of charge it pushes through itself. Real batteries also have internal resistance, so the voltage you actually measure across the terminals (terminal voltage) is usually a bit less than the emf once current is flowing. Emf shows up first in Topic 11.1 (Electric Current), and it comes back in a big way when you hit electromagnetic induction.

Why electromotive force matters in AP® Physics C: E&M

Emf lives in Topic 11.1 (Electric Current) in Unit 11, Electric Circuits. It's the answer to a question the whole unit depends on, which is what actually drives charge carriers around a circuit in the first place. Resistors, capacitors, and Kirchhoff's rules all assume something is supplying energy per unit charge, and that something is the emf source. When you write a loop equation, the emf is the term that raises the potential while every resistor drops it.

It also matters beyond circuits. In Unit 13, Faraday's law says a changing magnetic flux induces an emf, and that induced emf drives current in exactly the same energy-per-charge sense. If you understand emf cleanly in Unit 11, the induction unit feels like a natural extension instead of a brand-new idea.

How electromotive force connects across the course

Conventional Current (Unit 11)

Emf is the cause and conventional current is the effect. The source's emf sets up the potential difference that makes positive charge (by convention) flow from high to low potential through the external circuit. No emf source, no sustained current.

Drift Velocity (Unit 11)

Emf explains the energy side of current while drift velocity explains the motion side. The emf maintains an electric field inside the wire, and that field nudges electrons into their slow average drift. The two terms answer 'why do charges move?' and 'how fast do they actually move?'

Internal Resistance and Terminal Voltage (Unit 11)

Real batteries eat some of their own emf. With internal resistance r and current I, the terminal voltage is V = ℰ − Ir. This single equation is one of the most common ways AP problems test whether you know emf and terminal voltage aren't the same thing.

Faraday's Law and Induced emf (Unit 13)

A changing magnetic flux creates an induced emf, ℰ = −dΦ/dt. Same concept, different source. Instead of a chemical battery doing work on charges, a changing field does. Recognizing that induced emf plays the same circuit role as a battery's emf is the bridge between Units 11 and 13.

Is electromotive force on the AP® Physics C: E&M exam?

Emf shows up in two main ways. In Unit 11 circuit problems, you'll use ℰ in Kirchhoff's loop rule and in the terminal voltage equation V = ℰ − Ir, often deciding whether a measured voltage equals the emf (only when I = 0 or r = 0). Multiple-choice stems frequently target the concept directly, asking what provides the driving 'force' for charge carriers or what an emf source actually does in a circuit. The expected answer is energy per unit charge, not a literal force. In Unit 13, FRQs routinely ask you to calculate an induced emf from a changing flux and then treat it like a battery to find current. No released FRQ has needed the phrase 'electromotive force' defined verbatim, but you can't do circuit or induction FRQs without using ℰ correctly in your equations.

Electromotive force vs terminal voltage

Emf (ℰ) is the total energy per unit charge the source supplies. Terminal voltage (V) is the potential difference you'd actually measure across the battery's terminals while it operates. They differ because real batteries have internal resistance r, so when current I flows, V = ℰ − Ir. They're equal only when no current is drawn (open circuit) or the battery is ideal (r = 0). On the exam, if a problem mentions internal resistance, do not set the resistor voltage equal to the emf.

Key things to remember about electromotive force

  • Electromotive force (ℰ) is the energy per unit charge a source supplies to move charge through a circuit, measured in volts.

  • Despite the name, emf is not a force; it's a potential difference, and treating it as a force is a classic trap.

  • For a real battery with internal resistance r carrying current I, the terminal voltage is V = ℰ − Ir, so terminal voltage equals emf only when I = 0 or r = 0.

  • In Kirchhoff's loop rule, the emf source is the term that raises potential while resistors drop it around the loop.

  • Emf returns in Unit 13, where Faraday's law (ℰ = −dΦ/dt) describes an induced emf that drives current just like a battery does.

Frequently asked questions about electromotive force

What is electromotive force in AP Physics C?

Electromotive force (emf, ℰ) is the energy per unit charge a source like a battery provides to drive current through a circuit. It's measured in volts and appears first in Topic 11.1 (Electric Current).

Is electromotive force actually a force?

No. Emf is energy per unit charge (joules per coulomb), which makes it a potential difference measured in volts, not a force measured in newtons. The name is a historical leftover, and MCQs love testing this exact misconception.

What's the difference between emf and terminal voltage?

Emf is the total energy per charge the source supplies, while terminal voltage is what you measure across the battery's terminals during operation. With internal resistance r and current I, terminal voltage is V = ℰ − Ir, so it's less than the emf whenever current flows.

What does emf do for charge carriers in a circuit?

The emf source does work on charge carriers, raising their potential energy so they can flow through the circuit and lose that energy in resistors. It maintains the potential difference that keeps current going instead of dying out.

Where does emf show up besides batteries on the AP exam?

In Unit 13, a changing magnetic flux induces an emf according to Faraday's law, ℰ = −dΦ/dt. Induction FRQs typically have you compute this induced emf and then use it like a battery's emf to find current in a loop.