←
Key Equations

Key Equations

Potential energy of a two-charge system U(r)=keqQrU(r)=keqQr
Work done to assemble a system of charges W12⋯N=ke2∑iN∑jNqiqjrijfori≠jW12⋯N=ke2∑iN∑jNqiqjrijfori≠j
Potential difference ΔV=ΔUqorΔU=qΔVΔV=ΔUqorΔU=qΔV
Electric potential V=Uq=−∫RPE→⋅dl→V=Uq=−∫RPE→⋅dl→
Potential difference between two points ΔVAB=VB−VA=−∫ABE→·dl→ΔVAB=VB−VA=−∫ABE→·dl→
Electric potential of a point charge V=keqrV=keqr
Electric potential of a system of point charges VP=ke∑1NqiriVP=ke∑1Nqiri
Electric dipole moment p→=qd→p→=qd→
Electric potential due to a dipole VP=kep→·r^r2VP=kep→·r^r2
Electric potential of a continuous charge distribution VP=ke∫dqrVP=ke∫dqr
Electric field components Ex=−∂V∂x,Ey=−∂V∂y,Ez=−∂V∂zEx=−∂V∂x,Ey=−∂V∂y,Ez=−∂V∂z
Del operator in Cartesian coordinates ∇→=i^∂∂x+j^∂∂y+k^∂∂z∇→=i^∂∂x+j^∂∂y+k^∂∂z
Electric field as gradient of potential E→=−∇→VE→=−∇→V
Del operator in cylindrical coordinates ∇→=r^∂∂r+φ^1r∂∂φ+z^∂∂z∇→=r^∂∂r+φ^1r∂∂φ+z^∂∂z
Del operator in spherical coordinates ∇→=r^∂∂r+θ^1r∂∂θ+φ^1rsinθ∂∂φ∇→=r^∂∂r+θ^1r∂∂θ+φ^1rsinθ∂∂φ