Key Equations

Coulomb’s law	${\overrightarrow{\text{F}}}_{12}(r)=\frac{1}{4\pi {\epsilon }_0}\frac{q_1{q}_2}{r_{12}^2}{\widehat{\text{r}}}_{12}$
Superposition of electric forces	$\overrightarrow{\text{F}}(r)=\frac{1}{4\pi {\epsilon }_0}Q{\displaystyle \sum _{i=1}^N\frac{q_i}{r_i^2}}{\widehat{\text{r}}}_i$
Electric force due to an electric field	$\overrightarrow{\text{F}}=Q\overrightarrow{\text{E}}$
Electric field at point P	$\overrightarrow{\text{E}}(P)\equiv \frac{1}{4\pi {\epsilon }_0}{\displaystyle \sum _{i=1}^N\frac{q_i}{r_i^2}}{\widehat{\text{r}}}_i$
Field of an infinite wire	$\overrightarrow{\text{E}}(z)=\frac{1}{4\pi {\epsilon }_0}\frac{2\lambda }{z}\widehat{\text{k}}$
Field of an infinite plane	$\overrightarrow{\text{E}}=\frac{\sigma }{2{\epsilon }_0}\widehat{\text{k}}$
Dipole moment	$\overrightarrow{\text{p}}\equiv q\overrightarrow{\text{d}}$
Torque on dipole in external E-field	$\overrightarrow{\tau }=\overrightarrow{\text{p}}\times \overrightarrow{\text{E}}$