Electric Charges and Fields
What KSEAB tests here
Electric Charges and Fields covers Coulomb's law, superposition, electric field and field lines, the electric dipole, and Gauss's law with its standard applications. Questions are usually one-mark definitions, two-mark reasoning and three- or five-mark numericals on dipole fields or Gauss-law flux.
Core rules
- Charge is quantised, Q = ne, and conserved; induction explains the attraction of a neutral body.
- Coulomb force in vacuum: F = (1/4πε₀)q₁q₂/r², with 1/4πε₀ = 9×10⁹ N m² C⁻². In a medium, divide by the dielectric constant K.
- Field E = F/q₀ is a vector; field lines start on positive and end on negative charge, never cross, and their density indicates strength.
- Dipole moment p = q(2a), directed from −q to +q. Axial field = 2kp/r³; equatorial field = kp/r³ (opposite to p). Torque τ = pE sin θ.
- Gauss's law: Φ = q_enclosed/ε₀ over a closed surface. Results: line charge E = λ/(2πε₀r); infinite sheet E = σ/(2ε₀); inside a conductor E = 0.
Worked example
A dipole has p = 4×10⁻⁹ C m. Find the field on its axis at 0.20 m. E = 2kp/r³ = 2(9×10⁹)(4×10⁻⁹)/(0.20)³ = 72/8×10⁻³ = 9.0×10³ N C⁻¹, along p. Reasoning: the axial field carries the factor 2; cube the distance, not square it; convert cm to m first.
Traps that cost marks
Using r² in dipole formulas, forgetting direction (axial along p, equatorial opposite p), inserting the test charge into E, and quoting Gauss's law with a charge outside the surface. Flux through a closed surface depends only on enclosed charge, but E at a point depends on all charges.