Problem
Shielding and charge. A positive charge is placed outside a hollow metal conductor (uncharged) of arbitrary shape. (a) What happens to the charge distribution on the outer surface of the conductor? (b) What does a second charge inside the cavity perceive? (c) Why do the metal bodies of cars protect against lightning? Reason in terms of electric field and potential, without calculations.
Solution
(a) Redistribution on the outer surface. The field of the external charge sets the conductor’s free electrons in motion, and they arrange themselves until the electric field inside the metal becomes zero (the electrostatic equilibrium condition). Induced charges appear on the outer surface: negative in the region facing (attracted), positive in the opposite region. The net charge of the conductor remains zero — it is merely a separation (polarisation) of induced charges.
(b) Inside the cavity. The charge placed in the cavity perceives no field due to : the conducting shell acts as a shield. Since the field is zero throughout the thickness of the metal, Gauss’s theorem applied to a surface inside the metal that encloses the cavity requires that the external field not penetrate. The cavity is a region at constant potential, an electrically protected environment. This is the principle of the Faraday cage.
(c) The car and the lightning bolt. The car’s metal bodywork behaves as a closed conducting shell: during a lightning strike the charges distribute themselves over the outer surface and the field inside the cabin stays practically zero. The passengers, being inside the conducting cavity, are shielded, and the current flows along the outer surface to the ground without crossing the cabin. It is electrostatic shielding, not the tyres, that protects the occupants.
Links
Topics: Electric field and potential Concepts: Conductors in electrostatic equilibrium · Electric field