Electrostatics
Electrostatics covers Coulomb's law, electric field and potential, the dipole, Gauss's law and its applications, and capacitance including dielectrics and energy stored. The exam often pairs a Gauss's law derivation with a capacitor numerical.
Core rules
- Coulomb: F = (1/4πε₀) q₁q₂/r², with 1/4πε₀ = 9×10⁹ N m²/C². In a medium, divide by the dielectric constant K.
- Field of a point charge E = (1/4πε₀) q/r², directed away from positive charge. Potential V = (1/4πε₀) q/r is a scalar.
- Dipole moment p = q(2a), directed from −q to +q. Axial field 2kp/r³, equatorial field kp/r³; torque τ = pE sinθ, potential energy −pE cosθ.
- Gauss's law: flux through a closed surface = q(enclosed)/ε₀. It gives E = σ/ε₀ near a charged conductor and E = 0 inside it.
- Capacitance C = Q/V; parallel plate C = Kε₀A/d. Series: 1/C = Σ1/C(i). Parallel: C = ΣC(i).
- Energy stored U = ½CV² = ½QV = Q²/2C; energy density = ½ε₀E².
Worked example
A charge of 2 μC sits in air. At 0.30 m away, E = (9×10⁹ × 2×10⁻⁶)/(0.30)² = 1.8×10⁴/0.09 = 2×10⁵ N/C, and V = 9×10⁹ × 2×10⁻⁶/0.30 = 6×10⁴ V. Two capacitors of 2 μF and 3 μF in series give 6/5 = 1.2 μF.
Traps
- Adding capacitors in series as if they were resistors; they combine reciprocally.
- Using ½CV² and CV² interchangeably for stored energy.
- Forgetting that the field inside a conductor in electrostatic equilibrium is zero, so potential is constant throughout it.