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Key Equations

Potential energy of a two-charge system U(r)=keqQrU(r)=keqQr
Work done to assemble a system of charges W12N=ke2iNjNqiqjrijforijW12N=ke2iNjNqiqjrijforij
Potential difference ΔV=ΔUqorΔU=qΔVΔV=ΔUqorΔU=qΔV
Electric potential V=Uq=RPEdlV=Uq=RPEdl
Potential difference between two points ΔVAB=VBVA=ABE·dlΔVAB=VBVA=ABE·dl
Electric potential of a point charge V=keqrV=keqr
Electric potential of a system of point charges VP=ke1NqiriVP=ke1Nqiri
Electric dipole moment p=qdp=qd
Electric potential due to a dipole VP=kep·r^r2VP=kep·r^r2
Electric potential of a continuous charge distribution VP=kedqrVP=kedqr
Electric field components Ex=Vx,Ey=Vy,Ez=VzEx=Vx,Ey=Vy,Ez=Vz
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^1rφ+z^z=r^r+φ^1rφ+z^z
Del operator in spherical coordinates =r^r+θ^1rθ+φ^1rsinθφ=r^r+θ^1rθ+φ^1rsinθφ
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