University Physics Volume 2

# Key Equations

### Key Equations

 Potential energy of a two-charge system $U(r)=kqQrU(r)=kqQr$ Work done to assemble a system of charges $W12⋯N=k2∑iN∑jNqiqjrijfori≠jW12⋯N=k2∑iN∑jNqiqjrijfori≠j$ Potential difference $ΔV=ΔUqorΔU=qΔVΔV=ΔUqorΔU=qΔV$ Electric potential $V=Uq=−∫RPE→⋅dl→V=Uq=−∫RPE→⋅dl→$ Potential difference between two points $ΔVBA=VB−VA=−∫ABE→·dl→ΔVBA=VB−VA=−∫ABE→·dl→$ Electric potential of a point charge $V=kqrV=kqr$ Electric potential of a system of point charges $VP=k∑1NqiriVP=k∑1Nqiri$ Electric dipole moment $p→=qd→p→=qd→$ Electric potential due to a dipole $VP=kp→·r^r2VP=kp→·r^r2$ Electric potential of a continuous charge distribution $VP=k∫dqrVP=k∫dqr$ 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 $∇→=r^∂∂r+θ^1r∂∂θ+φ^1rsinθ∂∂φ∇→=r^∂∂r+θ^1r∂∂θ+φ^1rsinθ∂∂φ$