Electric potential is potential energy per unit charge

Electric potential (V) at a point in an electric field indicates the work needed to move a unit positive charge (+1 C) from infinity to that point. At infinity, electric potential is zero. As positive charges approach a positive source charge, they gain potential energy, while negative charges lose potential energy as they get closer.

The electric potential for a radial field around a point charge is expressed by:

$\text{V = }\frac{\text{Q}}{4\pi\epsilon_0 \text{r}}$

Where:

• V = electric potential (V)
• Q = magnitude of point charge (C)
• $\epsilon_0$ = permittivity of free space (8.85 x 10^-12 F m^-1)
• r = distance from point charge (m)

The sign of V depends on Q: positive for repulsive forces (positive Q) and negative for attractive forces (negative Q).

Worked example - Calculating electric potential near a point charge

A point charge of -3 x 10^-6 C is situated in a vacuum.

Calculate the electric potential 5 m away from this charge.

Step 1: Formula

$\text{ V = }\frac{\text{Q}}{4\pi\epsilon_0 \text{r}}$

Step 2: Substitution and correct evaluation

$V = \frac{-3 \times 10^{-6}}{4\pi \times 8.85 \times 10^{-12} \times 5}\text{ = -5,395.1 V}$

Electric potential energy

To change a charge's (q) electric potential energy, an external force must do work. The electric potential energy stored by charge q at a point is given by:

Electric potential energy = V q

Where:

• Electric potential energy (J)
• q = Charge (C)
• V = Electric potential (V)

Thus, electric potential conveys the electric potential energy per unit charge.

Worked example - Calculating electric potential energy

Calculate the electric potential energy of a charge of 1.5 x 10^-6 C placed in an electric field with a potential of 200 V.

Step 1: Formula

Electric potential energy = V q

Step 2: Substitution and correct evaluation

Electric potential energy = 200 x 1.5 x 10^-6 = 3 x 10^-4 J

Similarities and differences between gravitational and electric potential

Similarities:

• Both are governed by inverse square law forces (gravitational and Coulomb's law)
• Spherical masses and charges generate radially symmetric field lines.
• Both potentials, V, are defined as potential energy per unit mass/charge.
• V is zero at infinity for both gravitational and electric fields.

Differences:

Three main differences distinguish gravitational from electric potential:

• Gravitational forces are always attractive, whereas electric forces can be either attractive or repulsive.
• Electric fields can be shielded, but gravitational fields cannot.
• Electric forces are influenced by the medium, unlike gravitational forces.