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Conductors in electrostatic equilibrium exhibit several fundamental properties that are frequently tested in JEE.
First, E = 0 everywhere inside the conductor. If the field were non-zero, free electrons would move, contradicting equilibrium. This applies to the bulk material, not to cavities.
Second, all excess charge resides on the surface. Since E = 0 inside, Gauss's law with any internal Gaussian surface gives zero enclosed charge, meaning no charge exists in the interior.
Third, E at the surface is perpendicular to the surface and equals sigma/, where sigma is the local surface charge density. Any tangential component would cause surface charge to move.
Fourth, the surface is an equipotential. Since E is perpendicular to the surface, no work is done moving a charge along the surface, so the potential is constant.
Fifth, charge density is highest at points of greatest curvature (sharp points). For connected conducting spheres, sigma is proportional to 1/R. This explains corona discharge from lightning rods and St. Elmo's fire.
Electrostatic shielding: The interior of a hollow conductor is completely shielded from external electric fields. This is the Faraday cage effect. Conversely, a charge inside a cavity induces charges on the inner surface such that the field in the conductor remains zero.
Cavity with a charge: If charge Q is inside a cavity in a conductor, the inner surface of the conductor acquires charge -Q (induced), and the outer surface acquires additional charge +Q (by conservation). The field outside the conductor depends on the total charge of the system.