Electric Potential

This lesson covers: 

  1. Understanding electric potential as potential energy per unit charge
  2. The relationship between electric potential, charge, distance, and permittivity
  3. Calculating electric potential energy based on electric potential and charge size
  4. Similarities and differences between electric and gravitational potential

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:


V = 4πϵ0​rQ​


Where:

  • V = electric potential (V)
  • Q = magnitude of point charge (C)
  • ϵ0​ = 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

V = 4πϵ0​rQ​


Step 2: Substitution and correct evaluation

V=4π×8.85×10−12×5−3×10−6​ = −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.