Electrostatics — Formula Sheet

Electric field due to uniformly charged sphere

E = q/(4πε₀r²) outside the sphere, E = 0 inside

Electric field due to infinite line charge

E = λ/(2πε₀r) where λ is linear charge density

Electric potential V = W/q = work done per unit positive charge to bring from infinity

Potential due to point charge

V = q/(4πε₀r)

Potential energy of system of charges

U = (1/2)Σqᵢqⱼ/(4πε₀rᵢⱼ)

Electric field just outside conductor surface is perpendicular: E = σ/ε₀

Electric potential V = U/q represents work done per unit charge to bring a charge from infinity.

For point charge

V = q/4πε₀r.

For electric dipole with moment p⃗, potential at distance r is V = (1/4πε₀)(p cos θ/r²).

On axial line (θ = 0°): V = p/4πε₀r².