Electrostatics
What the exam tests
Electrostatics questions usually combine Coulomb forces, electric field and potential superposition, Gauss law, capacitance and energy stored in capacitors. Expect numericals with point charges, parallel plates, dielectric slabs and series or parallel capacitor networks.
Core rules
- Coulomb force between point charges is F = kq1q2/r^2, with k = 9×10^9 N m^2 C^-2 in vacuum; force is a vector along the line joining charges.
- Electric field E = F/q0; for a point charge E = kq/r^2. Field obeys vector superposition.
- Potential V = kq/r is a scalar; add potentials algebraically with signs. E = -dV/dr.
- Gauss law: flux through a closed surface is q_enclosed/ε0. Use symmetry to find fields of spheres, cylinders and sheets.
- Capacitance C = Q/V; parallel plate C = ε0A/d; with dielectric C = Kε0A/d. Series: 1/C = Σ1/Ci; parallel: C = ΣCi.
- Energy stored U = 1/2 CV^2 = Q^2/(2C).
Worked example
Two charges +4 μC and −2 μC are 0.30 m apart in vacuum. Find the field at the midpoint. Each is 0.15 m from the midpoint. Field due to +4 μC is 9×10^9×4×10^-6/(0.15)^2 = 1.6×10^6 N/C, directed away from it. Field due to −2 μC is 9×10^9×2×10^-6/(0.15)^2 = 0.8×10^6 N/C, directed toward it. If the positive charge is on the left, both fields point right, so the resultant is 2.4×10^6 N/C to the right.
Traps
Using the separation between charges instead of the distance to the field point is common. Potential must be added with signs, not as magnitudes. Gauss law applies only to closed surfaces, and the enclosed charge alone determines net flux. A dielectric reduces the field inside a capacitor but increases capacitance. Series capacitors carry the same charge, not the same voltage.