Electric Charge and Coulomb's Law

Rub a balloon on your hair and it picks up roughly $10^{-9}$ of its electrons’ worth of imbalance — enough to defy the gravity of the entire planet. Electricity is astonishingly strong; we only fail to notice because matter is almost perfectly neutral, positive and negative cancelling to exquisite precision.

Electric charge is a fundamental property of matter. There are two types: positive and negative.

Coulomb's law gives the force between two point charges:

$$\vec{F} = k_e\frac{q_1 q_2}{r^2}\hat{r}, \qquad k_e = \frac{1}{4\pi\varepsilon_0} = 8.99\times 10^9\;\text{N m}^2/\text{C}^2$$

Key properties of charge

• Quantised: $q = ne$ where $e = 1.602\times 10^{-19}$ C.
• Conserved: Total charge in an isolated system is constant.
• Like charges repel, opposite charges attract.

Superposition principle — The force on charge $q$ due to multiple charges is the vector sum:

$$\vec{F}_{\text{net}} = \sum_i \vec{F}_i = \sum_i k_e\frac{qq_i}{r_i^2}\hat{r}_i$$

Physics link: Coulomb's law has the same $1/r^{2}$ form as Newton's gravitational law. Both are inverse-square laws, but electric forces can be attractive or repulsive.

Common pitfall: Coulomb’s law gives the force between point charges. For extended objects, each piece pulls on each piece — you may only treat a sphere as a point at its centre because of a deep theorem, not because it is obvious.