Electrostatic potential

Lifting a stone stores energy that depends on its height. In the same way, moving a charge against an electric field stores energy, and potential tells you how much per unit charge.

Electrostatic potential V at a point = the work done per unit charge to bring a small positive test charge from infinity to that point, slowly. Unit: volt (1 V = 1 J/C).

For a point charge q: V = kq / r. Example: 1 nC at 30 cm gives V = 9 × 10⁹ × 10⁻⁹ / 0.3 = 30 V.

Potential is a scalar: a number with a sign, no direction. A negative charge gives a negative potential. So with many charges, just add the potentials as numbers, with their signs. This is far easier than adding field vectors.

What matters in practice is the potential difference. The work done by the field when a charge q moves from A to B is W = q(V_A – V_B). Example: 2 µC moving from 100 V to 20 V: W = 2 × 10⁻⁶ × 80 = 1.6 × 10⁻⁴ J.

This work does not depend on the path: the electrostatic force is conservative, like gravity. Only the start and end points matter.

Field and potential: E points in the direction in which V falls fastest. In a uniform field, E = V/d: a field of 1000 V/m means V drops by 1000 volts every metre.

Equipotential surfaces join points of equal V:

• Moving a charge along one needs no work.
• The field is always perpendicular to them.
• For a point charge they are spheres around it; for a uniform field they are parallel planes.