Key Equations

Potential energy of a two-charge system	$U(r)=k_e\frac{qQ}{r}$
Work done to assemble a system of charges	$W_{12\cdots N}=\frac{k_e}{2}{\displaystyle \sum _i^N{\displaystyle \sum _j^N\frac{q_i{q}_j}{r_{ij}}}}\text{for}i\ne j$
Potential difference	$\text{Δ}V=\frac{\text{Δ}U}{q}\text{or}\text{Δ}U=q\text{Δ}V$
Electric potential	$V=\frac{U}{q}=-{\displaystyle {\int }_R^P\overrightarrow{E}\cdot d\overrightarrow{l}}$
Potential difference between two points	$\text{Δ}{V}_{AB}=V_B-V_A=\text{−}{\displaystyle {\int }_A^B\overrightarrow{\text{E}}·d\overrightarrow{\text{l}}}$
Electric potential of a point charge	$V=\frac{k_{e}q}{r}$
Electric potential of a system of point charges	$V_P=k_e{\displaystyle \sum _1^N\frac{q_i}{r_i}}$
Electric dipole moment	$\overrightarrow{\text{p}}=q\overrightarrow{\text{d}}$
Electric potential due to a dipole	$V_P=k_e\frac{\overrightarrow{\text{p}}·\widehat{\text{r}}}{r^2}$
Electric potential of a continuous charge distribution	$V_P=k_e{\displaystyle \int \frac{dq}{r}}$
Electric field components	$E_x=-\frac{\partial V}{\partial x},E_y=-\frac{\partial V}{\partial y},E_z=-\frac{\partial V}{\partial z}$
Del operator in Cartesian coordinates	$\overrightarrow{\nabla }=\widehat{\text{i}}\frac{\partial }{\partial x}+\widehat{\text{j}}\frac{\partial }{\partial y}+\widehat{\text{k}}\frac{\partial }{\partial z}$
Electric field as gradient of potential	$\overrightarrow{\text{E}}=\text{−}\overrightarrow{\nabla }V$
Del operator in cylindrical coordinates	$\overrightarrow{\nabla }=\widehat{\text{r}}\frac{\partial }{\partial r}+\widehat{\mathit{\text{φ}}}\frac{1}{r}\frac{\partial }{\partial \phi }+\widehat{\text{z}}\frac{\partial }{\partial z}$
Del operator in spherical coordinates	$\overrightarrow{\nabla }=\widehat{\text{r}}\frac{\partial }{\partial r}+\widehat{\mathit{\text{θ}}}\frac{1}{r}\frac{\partial }{\partial \theta }+\widehat{\mathit{\text{φ}}}\frac{1}{r\text{sin}\theta }\frac{\partial }{\partial \phi }$