AP® Physics C: Electricity and Magnetism · Unit 10 · Topic 10.1

Cavities and Electrostatic Shielding

A charge placed inside a hollow cavity of a conductor induces an equal and opposite charge on the cavity wall, forcing the field inside the metal itself to zero while leaving the leftover charge to spread over the outer surface.

A conductor in equilibrium has zero electric field inside its own material, always. Free electrons are mobile, so they rearrange themselves until that condition holds. If you place a point charge +q inside a cavity carved out of a conducting shell, the field from that charge would poke into the metal unless something cancels it. Electrons in the metal shift toward the cavity wall nearest the charge, piling up until the inner surface carries exactly -q. That induced layer cancels the point charge's field everywhere inside the conducting material, which is the only region required to be field-free.

Charge conservation then takes over. The shell started neutral, so if the inner wall has -q, the outer surface must hold +q to keep the total at zero. If the shell already carried some extra charge Q, that extra charge joins the +q on the outside, since the inner surface's charge is pinned by the cavity charge alone and never changes. This is why the outer surface charge and field depend only on q and any net charge given to the shell, never on where the cavity charge sits or how the cavity is shaped. That independence is the real reason a car shell protects you in a lightning strike: current redistributes on the metal skin, and the field inside the passenger cavity stays zero regardless of the strike's exact path.

This separation of inner and outer surface charge sets up the next idea, grounding. Connect the shell to the ground and the outer charge can drain away or get replenished, decoupling the outside field from the cavity's contents entirely, while the inner surface still faithfully mirrors whatever sits inside.

Key terms

Electrostatic shielding
The blocking of external electric fields from the interior of a conductor by rearrangement of free charge.
Induced charge
Charge that appears on a conductor's surface in response to a nearby or enclosed charge, without any charge being added or removed.
Cavity
A hollow region carved out of a conductor, which is empty space even though it sits inside the conducting shell.
Gaussian surface
An imaginary closed surface drawn inside the conductor's material used to show the net enclosed charge, and hence field, must be zero there.

Watch it explained

  1. How it worksHow does a charge inside a metal cavity induce an opposite charge on the cavity wall?
  2. Worked exampleFind the charge on the inner and outer surfaces of a neutral shell with +6 nC in its cavity.
  3. Common mistakeWhy isn't the field inside a cavity zero when there is a charge sitting in the cavity?
  4. Going furtherWhat happens to the field outside a grounded shell when a charge sits in its cavity?

Check yourself

Your turn1 of 2
A conducting shell carries an extra net charge of +21 nC placed directly on it, in addition to a point charge of +20 nC sitting in its internal cavity. Find the charge that appears on the shell's outer surface, in nC.

End of topic.