# Electric Charge
- Charges come in two varieties, positive and negative.
- Net charge is the *algebraic sum* of an object's charges
- Protons and electrons have the same magnitude of charge (designated $1e$; a unit, **not** Euler's number)
	- The SI Unit of charge is the *Coulomb* (abbreviated C)
	- The smallest discrete quantity of charge is $\frac{1}{3}e$.
- In an isolated system, the net charge will always remain constant.

# Coulomb's Law
- Two charges will exert a force on each other along the line joining them.
	- The magnitude of this force is proportional to the *product of the charges* and inversely proportional to the to the $\sqrt{dist}$.
	- The equation to determine the force between two charges is as follows:
	$$ \vec{F}_{12} = \vec{r}k\frac{q_1q_2}{r^2} $$
		- $\vec{r}$ is a unit vector pointing from charge 1 to charge 2
		- $k$ is Coulomb's constant, or $8.99 * 10^9 \frac{Nm^2}{C^2}$ 
		- $q_1$ and $q_2$ are the charges
		- $r$ is the distance between those charges
		- The resulting force will push away if $q_1q_2$ is *positive*, and attract if $q_1q_2$ is negative. This is where the rule "opposites attract, like repels" comes from
- Coulomb's law only holds exactly true for *point charges* i.e a proton or electron.

# The Superposition Principle
The superposition principle states that:
> The net force acting on a point charge is equal to the sum of all individual forces.

This means that to find the net force acting on a single charge, you add up all of the individual forces acting on that charge.

# The Electric Dipole
An electric dipole consists of two point charges of equal magnitude but opposite sign. Many molecules behave like dipoles.
- **Electric dipole moment** ($p$) is defined as the product of the charge $q$ and the separation $d$ between the two charges making up the dipole. $p = qd$
- The dipole field at large distances decreases as the inverse *cube* of the distance. This is because the dipole has zero *net* charge.
- In an electric field, a dipole experiences a torque that aligns it with the field.
# Continuous Charge Distributions
It's largely impossible to sum the electric field from every particle in a piece of matter, so the approximation is made that the charge is spread continuously over the distribution.
- The number of dimensions involved changes the unit and terminology used:
	-  If the charge distribution extends throughout a *3d volume*, we describe it in terms of the **volume charge density** $\rho$, with units of $\frac{C}{m^3}$. 
	- For charge distributions spread over *surfaces*, we use **surface charge density** $\sigma$ ($\frac{C}{m^2}$).
	- For charge distributions spread over *lines*, we use **line charge density** $\lambda$ ($\frac{C}{m}$).
- To find the point charge, we can use this formula:
$$ \vec{E} = \int d \vec{E} = \int \frac{kdq}{r^2}\hat{r}$$
- 