Electrostatics
Electrostatics tests charge, Coulomb force, electric field and potential, Gauss law, conductors, and capacitors. Questions often require choosing between force, field, potential, and energy methods, so sign and vector discipline matter more than memorised formulas.
Core rules and concepts
- Coulomb force is F = k q1 q2 / r^2, directed along the line joining charges; like charges repel.
- Electric field E = F/q0 is a vector; potential V = W/q0 is a scalar. For a point charge, E = kq/r^2 and V = kq/r.
- In a uniform field, V = Ed, and E points from higher to lower potential.
- Gauss law: flux through a closed surface is q_enclosed/epsilon0. It is useful only with suitable symmetry.
- Inside a conductor in electrostatic equilibrium E = 0 and potential is constant; charge resides on the surface.
- Capacitance C = Q/V. For a parallel-plate capacitor C = epsilon0 A/d, multiplied by dielectric constant K when filled.
- Capacitors in series store equal charge; in parallel have equal voltage. Energy = 1/2 CV^2.
Worked example
Charges +2 microC and -2 microC are 0.10 m apart. At the midpoint, r = 0.05 m. Potentials add algebraically: k(2e-6)/0.05 + k(-2e-6)/0.05 = 0. Fields point the same way, from positive toward negative. Each magnitude is 9e9 x 2e-6 / 0.05^2 = 7.2e6 N/C, so total field is 1.44e7 N/C toward the negative charge.
Traps that cost marks
- Adding potentials as vectors or fields as scalars.
- Using Gauss law without symmetry, or including external charges in q_enclosed.
- Forgetting that capacitor series combinations have the same charge.
- Mixing microcoulomb and metre units, or dropping the sign of a charge.