Physics · Ch 1 — Electrostatics
Conductors at electrostatic equilibrium
Conductors at electrostatic equilibrium
A conductor contains a very large number of mobile charges -- in a metal, free electrons not bound to any particular atom -- that are free to move throughout the material. In the absence of an external field these free electrons move about randomly, with the material remaining, on average, electrically neutral throughout. When an external electric field is applied, or when the conductor is given a net charge, the free charges redistribute themselves rapidly until the conductor reaches a state called electrostatic equilibrium, in which the free charges are no longer, on average, moving. At electrostatic equilibrium, a conductor has several defining properties. First, the electric field is exactly zero everywhere inside the bulk of a conductor: if it were not, the remaining free charges would continue to experience a force and keep moving, contradicting equilibrium. Second, since the field inside is zero, any small Gaussian surface drawn entirely within the conductor's interior encloses zero net charge (by Gauss's law), meaning that any excess charge given to a conductor must reside entirely on its outer surface, never in its interior. Third, the field immediately outside a charged conductor's surface is always exactly perpendicular (normal) to the surface at every point, with magnitude E = sigma/epsilon0 (where sigma is the local surface charge density) -- a tangential component would keep driving surface charge to flow sideways, again contradicting equilibrium. …
What this figure shows. A solid conducting block is drawn with an external field applied around it; inside the block the field-line arrows are shown stopping abruptly at the conductor's boundary rather than continuing through the interior, indicating that the field inside the bulk of the conducting material is exactly zero once electrostatic equilibrium has been reached, even though a strong field exists in the f …
What this figure shows. A conductor with excess charge is drawn together with a small closed Gaussian surface positioned entirely within the conducting material, just below its outer surface. Because the field is zero everywhere inside the conductor (established using Figure 1.42's result), the flux through this interior Gaussian surface must also be zero, and by Gauss's law that forces the enclosed charge to be zero as well -- proving that any excess charge placed on a conductor cannot remain in its interior and must instead reside entirely on the conductor's o …
What this figure shows. A small patch of a charged conductor's surface is shown enlarged, with the field vector E drawn immediately outside that patch pointing straight out along the local surface normal, with no component running along (tangential to) the surface itself. If any tangential component existed, the free surface charges would keep flowing sideways along the surface under its influence, which contradicts the assumption that the conductor has already reached electrostatic equilibrium (no further charge motion); hence the field just outside a conductor's surface must be …