Field of infinite plane sheet

Intermediate

Uniform and independent of distance.

Key relationE = σ/2ε₀

E = σ/2ε₀ on each side, uniform and independent of distance. Two oppositely charged parallel plates give E = σ/ε₀ between them and zero outside.

Worked example

σ = 1 μC/m²: 56,500 N/C.

Common mistake

Valid near the middle of large sheets.

In more detail

An infinite plane sheet of charge with surface density σ produces a uniform field E = σ/(2ε0), independent of distance from the sheet.

Parallel-plate capacitors use nearly uniform fields between plates.
Modelling large charged surfaces in electrostatic experiments.
Parallel-plate capacitors give a nearly uniform field between their plates, which is useful in sensors and displays.

Why doesn't the field depend on distance?

Because the field lines spread out to cover the increasing area in a way that keeps the field constant.

Does a finite plate work the same?

Approximately, near the centre of a large plate.

Why is the field independent of distance from a sheet?

The contributions from distant parts of the sheet partially cancel, leaving a constant field near the surface.