University Physics Volume 2

# 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 $∇→=r^∂∂r+θ^1r∂∂θ+φ^1rsinθ∂∂φ∇→=r^∂∂r+θ^1r∂∂θ+φ^1rsinθ∂∂φ$
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