Electric charge is the intrinsic property of matter that makes it experience a force in an electric field. There are two kinds — positive (deficiency of electrons) and negative (excess of electrons) — and like charges repel while unlike charges attract. The SI unit of charge is the coulomb (C).
Three basic properties govern charge. (i) Quantisation: charge always comes in integer multiples of the elementary charge, $q=ne$ where $e=1.6\times10^{-19}\ \text{C}$ and $n$ is an integer. (ii) Conservation: the net charge of an isolated system never changes — charge can be transferred but not created or destroyed. (iii) Additivity: the total charge of a body is the algebraic sum of all the charges on it.
Coulomb's law gives the force between two stationary point charges $q_1$ and $q_2$ separated by a distance $r$ in vacuum:
$$F=\frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r^2}$$ where $\frac{1}{4\pi\epsilon_0}=9\times10^{9}\ \text{N}\,\text{m}^2\,\text{C}^{-2}$ and $\epsilon_0=8.85\times10^{-12}\ \text{C}^2\,\text{N}^{-1}\,\text{m}^{-2}$ is the permittivity of free space. The force is directed along the line joining the charges. In a medium of relative permittivity (dielectric constant) $K$, the force reduces to $F=\frac{1}{4\pi\epsilon_0 K}\frac{q_1q_2}{r^2}$.
When several charges act on a charge, the net force is the vector sum of the individual forces — this is the principle of superposition: $\vec{F}=\vec{F}_1+\vec{F}_2+\dots$
The electric field $\vec{E}$ at a point is the force per unit positive test charge placed there: $\vec{E}=\frac{\vec{F}}{q}$, with SI unit $\text{N/C}$ (or $\text{V/m}$). The field of a point charge $q$ at distance $r$ is $E=\frac{1}{4\pi\epsilon_0}\frac{q}{r^2}$, pointing radially outward for positive $q$.
- Field lines start on positive charges and end on negative charges; they never cross, and their density indicates field strength.
- An electric dipole is two equal and opposite charges $\pm q$ separated by $2a$, with dipole moment $\vec{p}=q(2a)$ directed from $-q$ to $+q$.
- On the axial line the field is $E_{axial}=\frac{1}{4\pi\epsilon_0}\frac{2p}{r^3}$; on the equatorial line $E_{eq}=\frac{1}{4\pi\epsilon_0}\frac{p}{r^3}$ (for $r\gg a$).
In a uniform field a dipole feels no net force but a torque $\tau=pE\sin\theta$ (i.e. $\vec{\tau}=\vec{p}\times\vec{E}$) that aligns it with the field. Finally, electric flux measures the number of field lines crossing a surface: $\phi=\vec{E}\cdot\vec{A}=EA\cos\theta$, a scalar with unit $\text{N}\,\text{m}^2\,\text{C}^{-1}$.