Potential difference (ΔV), or voltage, is the change in electric potential energy per unit charge between two points, equal to the negative line integral of the electric field along a path. In circuits, it's what drives current through resistors and what batteries and capacitors maintain across their terminals.
Potential difference is the work done per unit charge to move a charge between two points, measured in volts (1 V = 1 J/C). In Physics C terms, ΔV = -∫E·dl. That integral is the bridge between the field picture and the energy picture. If you know the electric field everywhere along a path, you can find the voltage between the endpoints, and vice versa (E = -dV/dx in one dimension).
The same quantity wears two costumes in this course. In electrostatics, it's a field concept you calculate from charge distributions like sheets, spheres, and slabs. In circuits, it's the 'push' a battery provides and the 'drop' that happens across each resistor or capacitor. Those are not two different things. A 6 V battery literally does 6 joules of work on every coulomb that passes through it, and that energy gets dissipated as charge falls through potential drops around the loop. Once that clicks, Kirchhoff's loop rule is just conservation of energy per charge.
Potential difference is arguably the single most-used quantity in AP Physics C: E&M because it appears in every unit. In Topic 1.5 you compute V from continuous charge distributions using ΔV = -∫E·dl. In Topic 2.3 it's the V in Q = CV, and watching whether V or Q stays constant is the whole game in dielectric problems. In Topics 3.1 and 3.2 it drives Ohm's law (ΔV = IR), Kirchhoff's loop rule, and power (P = IΔV). Even in Unit 4, moving charges through magnetic fields generates EMFs, which are potential differences by another name. If the exam had a most valuable player, ΔV would be it.
Keep studying AP Physics C: E&M Unit 2
Electric Field and Charge Distributions (Unit 1)
Potential difference is the integral of the field. The 2017 FRQ on a charged slab asked exactly this move, where you find E from Gauss's law and then integrate to get V. If you can go field-to-potential and back (E = -dV/dx), you've mastered half of Unit 1.
Dielectrics and Capacitance (Unit 2)
A capacitor stores charge at a potential difference, Q = CV. The classic trap is whether the capacitor stays connected to the battery (V constant) or is isolated (Q constant) when a dielectric slides in. The 2018 FRQ measured a dielectric constant using exactly this V-Q-C relationship.
Ohm's Law (Unit 3)
ΔV = IR is just potential difference doing its circuit job. Each resistor 'eats' some voltage, and the sum of drops around any loop equals the battery's EMF. Kirchhoff's loop rule is potential difference plus energy conservation.
Power in a Circuit (Unit 3)
P = IΔV says power is charge per second times energy per charge. That's why voltage is the natural energy currency of circuits. Combine it with Ohm's law and you get P = I²R and P = V²/R for resistors.
Potential difference shows up everywhere on the E&M exam, usually as a step inside a bigger problem rather than as the headline. The 2017 FRQ (charged slab) required integrating the electric field to find potential, the 2018 FRQ (dielectric experiment) used the voltage across parallel plates to extract a dielectric constant, and the 2019 FRQ asked for currents in a two-battery circuit, which is pure Kirchhoff loop-rule work with ΔV terms. In multiple choice, expect graph questions (slope of V vs. x gives -E), ranking tasks (which resistor has the biggest voltage drop), and capacitor scenarios where you decide whether V or Q is held fixed. The skill being tested is moving fluently between ΔV = -∫E·dl, ΔV = IR, and Q = CV depending on context.
EMF is the energy per charge a source like a battery supplies; potential difference is the energy per charge between any two points, including across resistors and real battery terminals. For an ideal battery they're equal, but a real battery with internal resistance r has terminal voltage ΔV = EMF - Ir, which is less than the EMF whenever current flows. The exam loves this distinction in circuit FRQs.
Potential difference is work per unit charge between two points, measured in volts, where 1 V equals 1 J/C.
ΔV = -∫E·dl connects the field picture to the energy picture, so knowing E along a path lets you compute the voltage between its endpoints.
In circuits, ΔV = IR for resistors and the sum of potential changes around any closed loop is zero (Kirchhoff's loop rule).
Power delivered or dissipated is P = IΔV, because current is charge per second and voltage is energy per charge.
For capacitors, Q = CΔV, and dielectric problems hinge on whether the voltage is held constant (battery connected) or the charge is (battery disconnected).
Terminal voltage of a real battery is less than its EMF when current flows, by the drop Ir across internal resistance.
It's the change in electric potential energy per unit charge between two points, measured in volts. Mathematically, ΔV = -∫E·dl, and in circuits it's the voltage that drives current through resistors via ΔV = IR.
Yes. 'Voltage' is just the everyday name for potential difference, and both are measured in volts. The exam uses ΔV or V interchangeably for the same quantity.
Electric potential (V) is a value assigned to a single point, and it depends on where you set V = 0. Potential difference (ΔV) is the difference between two points, which is what's physically measurable and what appears in ΔV = IR and Q = CV. Only differences in potential have physical meaning.
No. Potential energy (in joules) depends on the charge being moved, while potential difference (in joules per coulomb, or volts) is a property of the two points themselves. They're related by ΔU = qΔV, so a 2 C charge crossing a 6 V difference gains or loses 12 J.
Integrate the field along a path between the two points using ΔV = -∫E·dl. This is exactly what the 2017 FRQ on a charged slab required, where you first find E from Gauss's law and then integrate to get V. Going the other way, E = -dV/dx, so the field points downhill in potential.