Conductors and Insulators

A CONDUCTOR is any material containing a large population of FREE charge carriers -- in an ordinary metal, these are the valence (outermost-shell) electrons, which are only loosely bound to their parent nuclei and become genuinely free to drift through the material as soon as any external electric field is applied. Metals, the human body, the Earth itself, and animal bodies generally, are all conductors in this sense -- which is exactly why the human body offers a low-resistance path for current to flow through it from a live wire, producing the sensation of an electric shock described in section 8.7's opening.

Under ELECTROSTATIC conditions -- meaning once any transient charge movement has fully settled down and nothing is changing with time -- every conductor, of any shape, must obey five key properties, all of which follow logically from one another: (1) the net electrostatic field in the INTERIOR of a conductor is always exactly zero (if it were not, the free charges there would still be accelerating, contradicting the assumption of electrostatic equilibrium); (2) the potential is CONSTANT throughout the conductor's interior AND over its entire surface -- a direct consequence of property (1), since $E=-dV/dx=0$ everywhere inside means $V$ simply cannot change from point to point; (3) the interior of a conductor carries NO net charge at all -- any excess charge given to a conductor migrates entirely to its OUTER surface (this is exactly the fact exploited by the hollow-conductor property used in the Van de Graaff generator of section 8.13); (4) immediately OUTSIDE a charged conductor's surface, the field is always exactly PERPENDICULAR to that surface at every point (were there any component of field running ALONG the surface, the conductor's own abundant free surface charges would instantly redistribute themselves under it, until that component vanished -- again a restatement of electrostatic equilibrium); and (5) the surface charge DENSITY need not be uniform across a conductor's own surface -- it is generally much HIGHER at sharply curved regions such as points, spikes and edges than at broad, gently curved regions, which is the physical basis of both lightning rods and the corona-discharge spray brush used in the Van de Graaff generator. …