Electric potential is the work done per unit charge from infinity

Electric Fields & Potential — AQA A-Level Physics

Key Definition

Electric potential — The work done per unit charge in bringing a small positive test charge from infinity to that point. Measured in J C^-1 or V. It is a scalar quantity.

$$V = \frac{Q}{4\pi\varepsilon_0 r}$$

Where:
- $V$ = electric potential (V)
- $Q$ = source charge (C)
- $r$ = distance from centre (m)

Electric potentialThe work doneEnergy transferred when a force moves an object. In electrical circuits, W = QV (chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). times potential difference). per unit positive chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). in bringing a small test chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). from infinity to that point. is zero at infinity, just like gravitational potentialThe work doneEnergy transferred when a force moves an object. In electrical circuits, W = QV (charge times potential difference). per unit mass in bringing a small test mass from infinity to that point. Always negative. Measured in J kg⁻¹..
For a positive charge: V is positive, increases as you move closer.
For a negative charge: V is negative, decreases (more negative) as you move closer.
Unlike gravitational potentialThe work doneEnergy transferred when a force moves an object. In electrical circuits, W = QV (charge times potential difference). per unit mass in bringing a small test mass from infinity to that point. Always negative. Measured in J kg⁻¹. (always negative), electric potentialThe work done per unit positive charge in bringing a small test charge from infinity to that point. can be positive or negative depending on the sign of Q.
This equation also applies to a conducting sphere. Treat the charge as concentrated at the centre.
Potential is constant inside a charged sphere and decreases with distance outside.

Examiner Tips and Tricks

The potential always decreases in the same direction as the field lines.
If the field points from left to right, the potential drops from left to right.