Uniform Electric Fields

Between parallel charged plates the field is uniform, and the field strength is the potential difference divided by the separation:

E = V / d

so field strength can equally be measured in V m⁻¹ as in N C⁻¹. The two units are identical, which is a useful check that the relationship is consistent.

The force on a charge is constant throughout a uniform field:

F = E Q = Q V / d

independent of position between the plates. This makes the field the electrical equivalent of uniform gravity near the ground, and the motion works out the same way.

A charged particle fired into a uniform field — take it entering perpendicular to the field, like a projectile fired horizontally:

Along the initial direction — no force, so the velocity is constant.

Along the field — constant force, so constant acceleration, and the displacement grows as t².

The result is a parabolic path, exactly like a projectile under gravity. Every technique from Year 1 projectile work transfers directly.

Example: this is the basis of the deflection system in a cathode ray oscilloscope and of the inkjet printer, where charged droplets are steered onto the paper by the voltage across a pair of plates. It is also how the charge-to-mass ratio of the electron was first measured.

Comparison with the gravitational case — the acceleration is a = EQ/m, so unlike free fall it does depend on the particle's charge-to-mass ratio. An electron and a proton in the same field accelerate in opposite directions and at wildly different rates, the electron about 1836 times faster.

Energy gained across a potential difference — a charge accelerated through a p.d. V gains kinetic energy

E_k = Q V

which for an electron accelerated through one volt defines the electronvolt: 1 eV = 1.60 × 10⁻¹⁹ J. This is the natural energy unit for particle physics, where joules are inconveniently large.

Edge effects — the field bulges outwards near the edges of the plates, so the uniform approximation holds well only in the central region.