A conductor contains free electrons that can move under the influence of electric forces. When a conductor is placed in an external field or given a charge, these free electrons redistribute themselves rapidly until equilibrium is reached — a state where no net force acts on any charge and hence no current flows. In this equilibrium state, conductors have five key electrostatic properties that are absolutely essential for NEET.

Consider a conductor with some excess charge or placed in an external electric field. The free electrons immediately experience forces and begin moving. This movement continues until the electric field they create (opposing the original) exactly cancels the original field everywhere inside the conductor. At this point, net E = 0 inside and all motion stops (equilibrium). This happens extremely quickly — in ~10⁻¹⁹ seconds for metals.

A common misconception is that E = 0 means potential = 0. This is wrong. E = −dV/dr. If E = 0, then dV/dr = 0, meaning V = constant (not zero). The potential inside equals the surface potential and can be any value depending on the charge and geometry of the conductor.

Gauss's law states: total electric flux through any closed surface = Q_enclosed/ε₀. If we draw a Gaussian surface just inside the conductor surface (where E = 0 everywhere), then total flux = 0, so Q_enclosed = 0. This means no net charge can exist in the interior — all excess charge must be on the surface. For a hollow conductor, charge distributes only on the outer surface (not the inner cavity surface, unless the cavity contains a charge).

Using Gauss's law with a small cylindrical Gaussian surface ("pillbox") straddling the conductor surface:

This field varies from point to point on the surface — it is highest where surface charge density is highest. For a sphere, σ is uniform so E is the same everywhere on the surface. For an irregular conductor, charges accumulate more at sharp points and edges, leading to higher E at those locations. This is why lightning rods work — they have sharp tips where field is highest, causing preferential discharge.

An equipotential surface is one on which potential is the same at every point. Since the electric field is always perpendicular to equipotential surfaces (no work done moving along them), and the conductor surface has E perpendicular to it, the conductor surface is an equipotential surface. The entire conductor (interior + surface) is at the same potential — it is an equipotential body.

Field lines always cross equipotential surfaces at right angles. Near a conductor, equipotential surfaces are parallel to the conductor surface. Far from the conductor, equipotentials approach the spherical shape of a point charge. The spacing between equipotentials indicates field strength — closer spacing = stronger field.

Since E = 0 inside a conductor, the interior of a hollow conductor is completely shielded from external electric fields. This is electrostatic shielding. Practical applications: Faraday cage (metal cage shields electronics from external electromagnetic interference), coaxial cables (inner conductor shielded by outer conductor), and microwave ovens (metal walls prevent radiation from escaping). The shielding works only for static or slowly varying fields — not for very high-frequency radiation.

For an isolated spherical conductor: charge distributes uniformly over the surface. For an irregular conductor: charge density is highest at points with smallest radius of curvature (sharpest points) and lowest at flat or concave regions. This non-uniform distribution causes non-uniform electric fields outside the conductor. At sharp points, field can be high enough to ionise air — causing corona discharge (visible as a bluish glow).

For two connected conductors: charge distributes such that both are at the same potential. If a small sphere is connected to a large sphere, the small sphere (smaller capacitance) ends up at higher charge density — more charge per unit area — and hence higher E at its surface. Charge naturally flows to the larger sphere (lower potential for same charge) until equal potential is reached.

Capacitance C = Q/V, where Q is charge on the conductor and V is its potential. For an isolated spherical conductor of radius R: C = 4πε₀R. Larger conductor → higher capacitance → more charge for same potential. A parallel plate capacitor: C = ε₀A/d. With dielectric: C = Kε₀A/d where K is dielectric constant. Capacitors store energy: U = Q²/2C = CV²/2 = QV/2.