Electrostatics
Electrostatics deals with charges at rest: the forces between them, the electric field and potential they produce, and how conductors and dielectrics store charge in a capacitor. In Code 151 this unit is asked mostly as numericals - field or potential of a small charge system, energy stored in a capacitor, effect of a dielectric slab - plus one or two definition-plus-reasoning short answers, for example why electrostatic field lines cannot form closed loops or why the field just outside a charged conductor is σ/ε₀.
Core rules
- Coulomb's law: F = (1/4πε₀)·q₁q₂/r², with 1/4πε₀ = 9×10⁹ N m² C⁻²; use it in vector form when more than two charges act.
- Field of a point charge E = kq/r²; potential V = kq/r. Field is a vector, potential is a scalar with sign.
- Gauss's law: Φ = q(enclosed)/ε₀, valid for every closed surface; the flux depends only on the enclosed charge, never on charges outside.
- Field of an infinite plane sheet is σ/2ε₀, independent of distance; inside a hollow charged conductor E = 0 and charge sits on the outer surface.
- Parallel-plate capacitor: C = ε₀A/d; inserting a dielectric of constant K gives C′ = KC and reduces the field inside to E₀/K.
- Energy stored: U = ½CV² = ½QV = Q²/2C.
Worked example
A 2 μF capacitor is charged to 100 V. Find the charge and the stored energy. Q = CV = 2×10⁻⁶ × 100 = 2×10⁻⁴ C. U = ½CV² = ½ × 2×10⁻⁶ × 10⁴ = 1×10⁻² J = 10 mJ. Cross-check with U = ½QV: ½ × 2×10⁻⁴ × 100 = 10 mJ, so the arithmetic is consistent. If the charged capacitor is now isolated and a dielectric of K = 2 is inserted, Q stays 2×10⁻⁴ C while V falls to 50 V and U falls to 5 mJ.
Traps that cost marks
- Adding potentials as vectors; V is scalar, so add algebraically with signs.
- Writing the stored energy as CV² instead of ½CV².
- Assuming a dielectric changes the charge on an isolated capacitor.
- Quoting the field of an infinite sheet as σ/ε₀ and forgetting the factor ½.