Electrostatic Potential

In electrostatics, force describes how charges push or pull each other, but it is also useful for describing the energy state of a point in the electric field. The visible source explains that the work required to bring a test charge from infinity to a point helps define the electrostatic potential.

Core idea: Electrostatic potential tells how much work is required per unit positive charge to bring that charge from infinity to a given point in an electric field.

Electrostatic potential at a point is the work done by an external agent in bringing a unit positive test charge slowly from infinity to that point without acceleration.

The potential difference between two points P and R is the work done by an external force in moving a unit positive test charge from one point to the other.

If the work done in bringing charge q from infinity to point P is W, then

V_P ​= \[\frac {W​}{q}\]

If the potential energies at points P and R are U_P and U_R​, then

\[V_P-V_R=\frac{U_P-U_R}{q}\]

A point with higher electric potential is like a higher level in a gravitational field analogy. Just as a body tends to move from a higher gravitational potential to a lower gravitational potential, a positive charge naturally tends to move in the direction of decreasing electric potential.

Simple analogy

• Gravitational case: lifting a mass to a height stores gravitational potential energy.
• Electrostatic case: bringing a positive charge into an electric field configuration can require work, which is stored as electrostatic potential energy.