Electric Field Calculator

What is an electric field?

The electric field is the force that would act on a unit positive charge placed at a point: E = F / q. Its unit is the newton per coulomb (N/C) or, equivalently, the volt per metre (V/m). The field is a vector, pointing the way a positive charge at that point would be pushed.

Field of a point charge

At a distance r from a charge q the magnitude of the field is

E = k × |q| / r²

where k = 8.9876 × 10⁹ N·m²/C² is the Coulomb constant. The field points away from a positive charge and toward a negative one. Doubling the distance cuts the field to a quarter. The electric potential at the same point is V = k × q / r and carries the sign of the charge.

Force on a charge in a field

A charge q placed in a field of strength E feels a force F = q × E. A positive charge is pushed along the field and a negative charge against it.

Parallel plates

Between two wide parallel plates a distance d apart with a voltage V across them, the field is the same everywhere: E = V / d. It points from the positive plate to the negative plate.

Example

At 30 cm from a 5 nC charge, E = 8.9876 × 10⁹ × 5 × 10⁻⁹ / 0.3² = 499 N/C and the potential is 150 V. With 25 kV across plates 4 cm apart the field is 25 000 / 0.04 = 625 000 V/m, and a 0.5 µC charge in that field feels a force of 0.31 N.

Limits

The point charge formula is for vacuum and air. The parallel plate formula holds away from the edges. In air a spark jumps once the field exceeds roughly 3 × 10⁶ V/m. The fields of several charges have to be added as vectors.