Properties of Electric Charge

Electric charge is one of the fundamental properties of matter, like mass. Yet unlike mass, charge comes in two flavours and obeys some surprisingly strict rules. In this section we unpack the three foundational properties: quantization, conservation, and additivity.

Concept

Charge is a scalar quantity measured in coulombs ($C$). The SI prototype unit is enormous on the atomic scale: a single electron carries only $e = 1.602 \times 10^{-19}\,C$.

1. Quantization. Any observable charge must be an integer multiple of the elementary charge $e$: $Q = ne, \quad n \in \mathbb{Z}.$ This was first established by Millikan's oil-drop experiment. At the macroscopic level $n$ is so large that quantization is invisible — adding one electron to a $1\,C$ body changes the charge by one part in $10^{19}$.

2. Conservation. The total charge of an isolated system is invariant in time. Charges can be transferred from one body to another but cannot be created or destroyed. Even in nuclear reactions, the algebraic sum of charges before and after a process is preserved.

3. Additivity. Charge is a scalar that adds algebraically. If a system contains charges $q_1, q_2, \dots, q_n$, the net charge is $Q_\text{net} = \sum_{i=1}^{n} q_i.$ Unlike vectors, there is no need to worry about direction; only sign.

Derivation

To see quantization in action, consider rubbing a glass rod with silk. Some electrons are transferred from glass to silk. If $N$ electrons move, the glass acquires charge $+Ne$ and the silk acquires $-Ne$. The total change of the universe is $0$ — that is conservation.

Now suppose two identical conducting spheres carry charges $q_1$ and $q_2$. When brought into contact, charges redistribute until each sphere holds $q = \frac{q_1+q_2}{2}.$ This uses additivity (the total $q_1+q_2$ is preserved) and conservation (no charge leaks to the surroundings).

Worked Example

A body has a charge of $-3.2\,\mu C$. How many excess electrons does it carry?

We use $|Q| = ne$: $n = \frac{|Q|}{e} = \frac{3.2 \times 10^{-6}}{1.6 \times 10^{-19}} = 2 \times 10^{13}.$

Two further identical metal spheres carry $+6\,\mu C$ and $-2\,\mu C$. After contact each will hold $q = \frac{+6 + (-2)}{2}\,\mu C = +2\,\mu C.$

Common Confusions

• "Charge can be any real number." No — only integer multiples of $e$ are physically realised. Quarks have fractional charge $\pm e/3, \pm 2e/3$ but are never observed in isolation.
• Conservation is not the same as constancy. The charge of a particular body can change (by transfer), but the total of an isolated system cannot.
• Charge is not relativistically variable. Unlike mass, $q$ is the same in every inertial frame.
• Additivity is algebraic. Equal positive and negative charges sum to zero net charge, even though the body is not discharged — it is electrically neutral, with internal charges still present.

Key Takeaways

• $Q = ne$ where $n$ is an integer and $e = 1.6\times 10^{-19}\,C$.
• Charge is conserved in any isolated process, classical or quantum.
• Charge is a scalar; net charge is the algebraic sum of individual charges.
• For two identical conducting spheres in contact, charges redistribute to the mean value.