Conductors, Capacitors, and Dielectrics: every key term you need (+ practice quiz)

More AP Physics C: E&M guides

• Electric Circuits
• Magnetic Fields and Forces
• Electromagnetic Induction and Maxwell's Equations

Electrostatic Equilibrium

The state in which no net charge motion occurs inside a conductor; requires E = 0 everywhere in the conducting material.

Field Inside a Conductor

Zero in equilibrium — any interior field would push free electrons until their rearrangement cancels it.

Charge on a Conductor

All excess charge resides on the outer surface of a conductor in equilibrium; Gauss's law with an interior surface proves the interior holds none.

Conductor as Equipotential

Every point of a conductor in equilibrium is at the same potential, since E = 0 inside means no potential difference between points.

Field at a Conductor Surface

Just outside a charged conductor, E = σ/ε₀, perpendicular to the surface; a parallel component would drive surface currents.

Charge and Curvature

Surface charge density is largest where a conductor is most sharply curved, making fields strongest at points and edges — the basis of lightning rods.

Cavity in a Conductor

An empty cavity inside a conductor is field-free; the conductor shields its interior from external static fields (Faraday cage).

Induced Charge on Cavity Wall

A charge +q placed inside a cavity induces −q on the cavity wall and +q on the conductor's outer surface, keeping the metal's interior field zero.

Capacitor

Two conductors carrying equal and opposite charge ±Q; stores charge and energy in the electric field between them.

Capacitance

C = Q/V — the charge stored per volt of potential difference; depends only on geometry and dielectric, not on Q or V themselves.

Parallel-Plate Capacitor

C = κε₀A/d: capacitance grows with plate area, shrinks with plate separation, and multiplies by the dielectric constant κ.

Farad

SI unit of capacitance, 1 F = 1 C/V; practical capacitors are usually microfarads (μF) or picofarads (pF).

Deriving C for a Geometry

Recipe: put ±Q on the conductors, find E via Gauss's law, integrate V = −∫E·dl between them, then compute C = Q/V.

Cylindrical Capacitor

Coaxial cylinders of radii a and b: C = 2πε₀L/ln(b/a), from integrating the 1/r field of the inner cylinder.

Spherical Capacitor

Concentric spheres of radii a and b: C = 4πε₀ab/(b−a); as b → ∞ this gives an isolated sphere C = 4πε₀a.

Energy Stored in a Capacitor

U = ½QV = ½CV² = Q²/(2C) — the work done moving charge against the growing potential difference.

Energy Density of E Field

u = ½ε₀E² joules per cubic meter; energy is stored in the field itself, a result derivable from the parallel-plate case.

Capacitors in Parallel

Same voltage across each; charges add, so C_eq = C₁ + C₂ + … — equivalent to enlarging the plate area.

Capacitors in Series

Same charge on each; voltages add, so 1/C_eq = 1/C₁ + 1/C₂ + … — equivalent capacitance is smaller than any individual one.

Dielectric

An insulating material placed between capacitor plates; its molecules polarize, reducing the net field and raising capacitance by factor κ.

Dielectric Constant κ

Dimensionless factor (κ ≥ 1) by which a dielectric multiplies capacitance and divides the field of fixed free charge: C = κC₀.

Induced Surface Charge

Polarized dielectric develops bound charge on its faces opposing the free charge on the plates, weakening the interior field to E₀/κ.

Dielectric Breakdown

If the field exceeds a material's dielectric strength, it ionizes and conducts — sparks in air occur near 3×10⁶ V/m.

Isolated Capacitor + Dielectric

With the battery disconnected, Q is fixed: inserting a dielectric leaves Q unchanged, drops V and E by κ, and decreases stored energy (the slab is pulled in).

Connected Capacitor + Dielectric

With the battery attached, V is fixed: inserting a dielectric keeps V, multiplies Q and stored energy by κ, with the battery supplying the extra charge.

Work to Charge a Capacitor

Moving charge dq across potential q/C requires dW = (q/C)dq; integrating from 0 to Q gives U = Q²/(2C).

Grounding

Connecting a conductor to the Earth, an effectively infinite charge reservoir at V = 0; charge flows until the conductor reaches ground potential.

Electrostatic Shielding

A conducting enclosure keeps external static fields out of its interior; sensitive electronics are housed in grounded metal cases for this reason.

Method of Symmetry for Conductors

Field lines meet conductor surfaces at right angles, and conductors distort nearby fields so their surfaces remain equipotentials.

Capacitor Charge Redistribution

When charged capacitors are reconnected, charge is conserved at each isolated node and flows until connected plates reach a common potential.

Effect of Halving Plate Separation

For a parallel-plate capacitor, halving d doubles C; at fixed Q, V halves and stored energy halves; at fixed V, Q and U double.

Polarization vs Conduction

Conductors cancel internal fields with free charge motion; dielectrics only partially reduce fields via bound-charge alignment of molecular dipoles.