Uniform electric fields and their applications

Electric force and the motion of a charge

The electric force

A charge q placed in a field E experiences a force:

F = q * E

If q > 0, F is in the same direction as E.
If q < 0, F is in the opposite direction to E.

The magnitude of the force is F = |q| * E, expressed in newtons (N) if q is in coulombs (C) and E in V/m.

Example: an electron between two plates

An electron (q = -1.6 × 10⁻¹⁹ C) is placed in a field E = 10⁵ V/m.

F = 1.6 × 10⁻¹⁹ × 10⁵ = 1.6 × 10⁻¹⁴ N

This force is directed in the opposite direction to E, as the electron’s charge is negative.

Motion in a uniform field

In a uniform field, the electric force is constant (same direction, sense and magnitude everywhere). According to Newton’s second law, a charged particle of mass m undergoes constant acceleration:

a = F / m = q * E / m

Its motion is therefore analogous to free fall: a straight-line trajectory if the initial velocity is parallel to E, or a parabolic trajectory if it enters with an initial velocity perpendicular to the field (like a projectile).

Application

In certain devices (oscilloscopes, inkjet printers), a beam of charged particles passes through a uniform electric field created by two plates: the observed deflection allows the field or the charge of the particles to be measured.

Common pitfall