Study Notes: Conductors and Capacitors

Electrostatic Equilibrium

A state where all net charge movements have ceased; no net current flows inside the conductor.

Conductor

A material (usually a metal like copper or aluminum) containing free charge carriers (electrons) that can move.

Electric Field Inside a Conductor

In electrostatic equilibrium, the electric field inside a conductor is zero (E_inside = 0).

Equipotential Volume

A conductor in electrostatic equilibrium is an equipotential volume, meaning the electric potential is constant throughout.

Surface Electric Field Direction

The electric field just outside a charged conductor is always perpendicular to the surface.

Gauss's Law

A law stating that the electric flux through a closed surface is proportional to the charge enclosed.

Surface Charge Density (σ)

The amount of charge per unit area on the surface of a conductor.

Permittivity of Free Space (ε₀)

A physical constant describing how electric fields interact with a vacuum (approximately 8.85×10⁻¹² F/m).

Electrostatic Shielding

The phenomenon where a conductor blocks external electric fields inside its cavity.

Induced Charge

The charge that appears on the surface of a conductor in response to an external electric field or charge nearby.

Charge Distribution on Conductors

For conductors in electrostatic equilibrium, excess charge resides entirely on the surface.

Electrostatic Potential (V)

The work done per unit charge to move a charge from infinity to a point in an electric field.

Field Condition Inside a Conductor

The electric field inside a conductor in electrostatic equilibrium is zero (E = 0).

Potential Difference (ΔV)

The difference in electric potential between two points; related to electric field via ΔV = -∫E·dl.

Curvature and Charge Density (σ)

On an irregularly shaped conductor, surface charge density is greater at points with smaller radius of curvature.

Gaussian Surface

A closed surface used in Gauss's Law to calculate electric flux and enclosed charge.

Electric Field Just Outside Surface

The electric field just outside a charged conductor is given by E_surface = σ/ε₀.

Sharp Points of Conductors

Regions of high charge density that produce strong electric fields due to their small radius of curvature.

Conductor with Hollow Cavity (Empty)

In a hollow conductor with no charge inside, the electric field inside the cavity is zero.

Charge in Hollow Cavity

When a conductor surrounds a point charge in its cavity, the inner surface acquires an equal and opposite charge.

Common Pitfall: Potential vs Electric Field

Confusing that since E=0 inside a conductor, V must also be zero; in fact, V is constant.

Infinite Sheet Electric Field Error

Mistakenly apply E = σ/2ε₀ for fields involving conductors, when the correct formula is E = σ/ε₀.

Touching Conductors Charge Sharing

Conductors in contact share charge until their potentials are equal, not necessarily their total charges.

Cavity Charge Induction

A charge inside a cavity induces a real charge on the inner surface of the conductor.