Key Equations

Coulomb’s law	${\vec{F}}_{12} (r) = \frac{1}{4 π ε_{0}} \frac{q_{1} q_{2}}{r_{12}^{2}} {\hat{r}}_{12}$
Superposition of electric forces	$\vec{F} (r) = \frac{1}{4 π ε_{0}} Q \sum_{i = 1}^{N} \frac{q_{i}}{r_{i}^{2}} {\hat{r}}_{i}$
Electric force due to an electric field	$\vec{F} = Q \vec{E}$
Electric field at point P	$\vec{E} (P) \equiv \frac{1}{4 π ε_{0}} \sum_{i = 1}^{N} \frac{q_{i}}{r_{i}^{2}} {\hat{r}}_{i}$
Field of an infinite wire	$\vec{E} (z) = \frac{1}{4 π ε_{0}} \frac{2 λ}{z} \hat{k}$
Field of an infinite plane	$\vec{E} = \frac{σ}{2 ε_{0}} \hat{k}$
Dipole moment	$\vec{p} \equiv q \vec{d}$
Torque on dipole in external E-field	$\vec{τ} = \vec{p} \times \vec{E}$