Quantisation of Charge

The Core Idea: Charge Comes in Packets

All observable electric charge in nature is quantised. This means charge cannot have any arbitrary value; it exists only in discrete, indivisible packets. The size of this fundamental packet is the charge of a single electron or proton.

The Quantisation Rule

Experimentally, every free charge $q$ on any object is an integral multiple of a basic unit of charge $e$.

• $q$ : Total charge on the body.
• $n$ : Any integer (…, -2, -1, 0, 1, 2, …). Positive $n$ means net positive charge; negative $n$ means net negative charge.
• $e$ : The elementary charge, the magnitude of charge on a single electron or proton.

By convention:

• Charge on an electron: $-e$
• Charge on a proton: $+e$

The Value of the Elementary Charge

In the SI system, the elementary charge is:

This means that one coulomb of charge contains approximately $6 \times 10^{18}$ electrons.

Why Quantisation is Invisible in Daily Life

At the macroscopic level, the charges we handle (e.g., a few microcoulombs, $1 \ \mu\text{C} = 10^{-6} \ \text{C}$) are enormous compared to $e$. For example, a charge of $1 \ \text{mC}$ contains roughly $10^{13}$ times $e$. Because the step size $e$ is so tiny, the charge appears to change continuously — like a dotted line that looks solid from a distance.

Practical consequence: Quantisation of charge can be ignored in macroscopic electrostatics. It becomes important only at the microscopic level, where charges are of the order of tens or hundreds of $e$. …