Electric Charge & Coulomb's Law Cheat Sheet

Key Facts

• Like charges repel and opposite charges attract, so two positive charges or two negative charges push apart, while a positive and a negative charge pull together.
• Electric charge is conserved, meaning the total charge of an isolated system stays constant: $q_{\text{total, before}} = q_{\text{total, after}}$.
• Charge is quantized in multiples of the elementary charge: $q = ne$, where $e = 1.60 \times 10^{-19}\ \text{C}$ and $n$ is an integer.
• Coulomb's law for the magnitude of electric force is $F = k\frac{|q_1q_2|}{r^2}$, where $k = 8.99 \times 10^9\ \text{N}\cdot\text{m}^2/\text{C}^2$.
• The electric force gets weaker with distance according to an inverse-square relationship, so doubling $r$ makes the force $\frac{1}{4}$ as large.
• The force on charge $q_1$ due to charge $q_2$ has the same magnitude as the force on $q_2$ due to $q_1$, but the forces point in opposite directions.
• For multiple charges, use superposition: $\vec{F}_{\text{net}} = \vec{F}_1 + \vec{F}_2 + \vec{F}_3 + \cdots$.
• A neutral object has equal amounts of positive and negative charge, so its net charge is $q_{\text{net}} = 0$.

Vocabulary

Electric charge

A property of matter that causes electric forces and can be positive, negative, or zero.

Coulomb

The SI unit of electric charge, written as $\text{C}$.

Elementary charge

The smallest basic unit of free charge, with magnitude $e = 1.60 \times 10^{-19}\ \text{C}$.

Coulomb's law

The rule that gives the electric force between two point charges: $F = k\frac{|q_1q_2|}{r^2}$.

Conductor

A material in which electric charges can move easily, such as copper or aluminum.

Insulator

A material in which electric charges do not move easily, such as rubber, glass, or plastic.