Electrostatic Potential and Capacitance — Formula Sheet

Potential Energy Difference

ΔU = U_P − U_R = W_RP (work done by external force in moving charge q from R to P).

The reference point for potential energy is taken at infinity where potential energy = 0.

Potential due to a point charge Q at distance r

V = kQ/r = Q/(4πε₀r). This falls as 1/r.

No work is done in moving a charge along an equipotential surface (since ΔV = 0, W = qΔV = 0).

For two charges

U = kq₁q₂/r₁₂. Positive U means repulsive (like charges); Negative U means attractive (unlike charges).

For three charges

U = k[q₁q₂/r₁₂ + q₁q₃/r₁₃ + q₂q₃/r₂₃]. Sum over all PAIRS.

For a point charge Q at the origin, the potential at distance r is: V(r) = (1/4πε₀) × (Q/r).

An electric dipole consists of charges +q and -q separated by distance 2a, with dipole moment p = 2qa.

The total potential at a point due to a system of charges is the algebraic sum of potentials due to individual charges: V = Σ (1/4πε₀) × (qᵢ/rᵢ).