Electric potential difference (ΔV) is the change in electric potential energy per unit charge between two points in an electric field, equal to the negative line integral of the field: ΔV = -∫E·dl. Measured in volts (J/C), it tells you the work needed to move charge between those points.
Electric potential difference, written ΔV, is the change in electric potential energy per unit charge as a charge moves between two points in an electric field. In plain terms, it answers the question "how much work per coulomb does it take to push a positive test charge from point A to point B?" The unit is the volt, which is just a joule per coulomb.
In AP Physics C: E&M, the calculus version is what matters. Potential difference is the negative line integral of the electric field along a path: ΔV = -∫E·dl. Flip it around and the field is the negative gradient of potential, E = -dV/dx in one dimension. The negative sign carries real physics. The electric field always points from high potential toward low potential, so positive charges naturally "fall" toward lower potential, just like a ball rolls downhill. Because the electrostatic force is conservative, ΔV between two points doesn't depend on the path you take, only on the endpoints.
This concept lives in Unit 1 (Electrostatics, topic 1.1) and it's the bridge between the force picture and the energy picture of electrostatics. Coulomb's law and electric fields tell you about forces; potential difference lets you use energy conservation instead, which is usually faster. The relationship ΔU = qΔV converts volts into joules, so you can find the speed of an accelerated charge without ever touching kinematics in a field.
It also doesn't stay in Unit 1. Potential difference is the same quantity you'll call voltage when you hit circuits, it defines capacitance (C = Q/ΔV), and it's the reason a conductor in equilibrium is an equipotential. If you can move comfortably between E, V, and U, you've unlocked most of the E&M exam.
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Electric Potential (Unit 1)
Electric potential V is the value at a single point (relative to a chosen reference, usually infinity), while potential difference ΔV compares two points. Only differences are physically measurable, which is why you're free to set V = 0 wherever it's convenient.
Electric Fields (Unit 1)
Field and potential difference are two views of the same thing. ΔV = -∫E·dl turns a field into a potential difference, and E = -dV/dx turns potential back into a field. On FRQs you'll constantly hop between them, so know which derivative or integral goes which direction.
Voltage (Unit 2)
Voltage in circuits IS electric potential difference, just measured across batteries, resistors, and capacitors instead of points in space. Kirchhoff's loop rule is really just the statement that ΔV around a closed path is zero because the electrostatic field is conservative.
Conservation of Charge (Unit 1)
Potential difference tells you how charge wants to move, and conservation of charge tells you charge is never created or destroyed while it moves. Together they explain why charge redistributes on conductors until the whole surface sits at one potential.
Expect to compute ΔV from a field, not just quote a formula. The 2017 FRQ (Q1) gave a nonconducting slab with uniform volume charge density ρ₀ and asked for the field via Gauss's law, with potential analysis following from integration of that field. That's the classic pattern: derive E(x) for a charge distribution, then integrate -∫E·dl to get the potential difference between two locations. MCQs test the conceptual side, like which direction E points relative to increasing potential, why ΔV is path-independent, and the energy relation ΔU = qΔV. Watch your signs. The negative sign in ΔV = -∫E·dl and the sign of the charge in W = qΔV are the two most common point-losers.
Electric potential V is assigned to a single point in space and depends on where you put your zero reference (usually infinity). Electric potential difference ΔV is the gap between two points, and it's the only one a voltmeter can actually measure. Think of it like elevation versus the height of a staircase. The elevation depends on what you call sea level; the height of the stairs doesn't.
Electric potential difference is the work done per unit charge to move a positive test charge between two points, measured in volts (joules per coulomb).
The calculus relationship is ΔV = -∫E·dl, and going the other way, E = -dV/dx, so the field points from high potential to low potential.
Because the electrostatic force is conservative, ΔV between two points is path-independent, which is what makes Kirchhoff's loop rule work later in circuits.
The energy connection ΔU = qΔV lets you use conservation of energy to find speeds and kinetic energies of charges, which is usually faster than working with forces.
Only potential differences are physically meaningful; the potential at a single point depends on your choice of reference, so you can set V = 0 wherever it's convenient.
On FRQs, a common move is to derive E from Gauss's law for a charge distribution, then integrate it to find the potential difference between two points.
It's the change in electric potential energy per unit charge between two points in an electric field, calculated as ΔV = -∫E·dl and measured in volts (J/C). It tells you the work per coulomb needed to move a charge between those points.
Yes. Voltage is just the everyday name for electric potential difference, especially in circuits. When you say a battery is 9 V, you mean there's a 9 J/C potential difference between its terminals.
Potential V is the value at one point relative to a chosen reference (usually V = 0 at infinity), while potential difference ΔV compares two points. Only ΔV is directly measurable, which is why the reference choice never affects the physics.
From high to low potential. That comes from E = -dV/dx, the negative gradient. A positive charge released in a field moves toward lower potential, losing potential energy and gaining kinetic energy.
Because moving a positive charge against the field requires positive work, which raises its potential. The negative sign encodes that the field points in the direction of decreasing potential. Dropping it is one of the most common sign errors on E&M free-response questions.