Field of a charged shell

Intermediate

Zero inside, point-like outside.

Outside a uniformly charged spherical shell the field equals that of a point charge at the centre; inside it is zero. The same holds for gravity.

Worked example

Charge on a hollow metal sphere sits on the outside.

Common mistake

Not the same for non-spherical shapes.

In more detail

Outside a uniformly charged spherical shell, the field is as if all the charge were at the centre, E = kQ/r². Inside the shell, the field is zero.

The shell theorem applies to atoms and planets in electrostatics.
Faraday cages rely on the zero field inside a charged conductor.
A charged metal ball in a lab behaves like a point charge far away, but has no field inside it.

Why is the field zero inside?

Because the forces from all parts of the shell cancel for a point inside.

Does it apply for a solid sphere?

Outside, yes. Inside a solid sphere, the field depends on the enclosed charge.

Why is the field zero inside a charged shell?

Charges on opposite sides of the shell pull in opposite directions, and their fields cancel at any point inside.