Electric charge

Electrical charge is a fundamental property of matter.

SI Unit

The SI unit of electrical charge is Coulomb (C), named after French physicist Charles Augustine de Coulomb.

Charge of subatomic particles

Particle	Symbol	Absolute charge (Coulombs)	Relative charge (to proton)
proton	$p^+$	$+1.602 \times 10^{-19}$	+1
neutron	$n^0$	0	0
electron	$e^-$	$-1.602 \times 10^{-19}$	−1

Properties

Quantisation

Any electrical charge is a whole multiple of $e \equiv 1.602 \cdot 10^{-19} C$.

i.e.,

$$ \forall Q, Q=ae, a \in Z $$

Restricted type

A charge must be either positive or negative.

Positive and negative charges can cancel each out, therefore the total charge of a system is the algebraic sum of charges of all its elements.

i.e., $$ Q_{system}=\sum Q_{element} $$

Warning: This does not mean the entire system can be always approximated as a point charge of $\sum Q_{elements}$, as the distribution of charges heavily influence the electrostatic behaviour of a system.

Conservation

Charge can neither be created or destroyed but only transfered. The amount of charge in any closed system is constant.

i.e.,

$$\sum Q = C$$

where C is a constant for any closed system.

Electrostatic force

Any charge exert an electrostatic force on any other charge.

This phenomenon is described by Coulomb's law:

$$\vec F_{e}(B \to A)=-\frac{1}{4\pi \epsilon_0}\frac{Q_AQ_B}{\left\| AB \right\|^2}\widehat{AB}$$

where $A$,$B$ are point charges

Charge density

For a thin, long conductor (e.g., electric cable):

$$\text{charge density } \lambda = \frac{dQ}{dL}$$

For a thin surface (e.g., aluminium foil):

$$\text{charge density } \sigma = \frac{dQ}{dA}$$