Electric Charge

Source lecture(s): SC134 Lec1

Intuition

Charge is the source of electric forces. It comes in two flavors, positive and negative, and obeys strict conservation laws.

Formal Definition

Electric charge $q$ is a scalar property of matter that produces and responds to electric fields. The elementary charge is $e=1.60\times10^{-19}\,\text{C}$.

Mathematical Formulation

\[Q = ne$$ Coulomb's law: $$F = \frac{1}{4\pi\varepsilon_0}\frac{|q_1 q_2|}{r^2}\]

Derivation

Coulomb's law was determined experimentally by torsion balance. The $1/4\pi\varepsilon_0$ factor ensures consistent units in SI.

Worked Example

Two protons 1 nm apart repel with $F\approx 2.3\times10^{-10}\,\text{N}$.

Common Mistakes

Treating charge as a vector.
Forgoing the absolute value when computing magnitude.

Quiz

Q1. What is the SI unit of charge?

Answer

Coulomb (C).

Q2. How many electrons make $-1\,\mu$C?