Mathwizurd.com is created by David Witten, a mathematics and computer science student at Vanderbilt University. For more information, see the "About" page.

# Introduction

The College Board releases a list of topics on the AP Physics Exam. In this study guide, I will be going over each one, including a potential problem that could come up.

# Electrostatics

## Charge and Coulomb's Law

MathJax TeX Test Page Really basically, charge is the quantity that causes it to experience a force in an electric field. Coulomnb's law expresses the force felt by a charge from another charge. $$F = \dfrac{kq_1q_2}{r^2}$$

### Possible Problem

Three charges in a line. What's the force on the first one? When doing this, keep in mind that force is a vector, so focus on the direction.

## Electric Field and Electric Potential

MathJax TeX Test Page Electric field is a vector field that applies forces to other charged particles. Potential energy equals the integral of force. So, if force = $\dfrac{kq_1q_2}{r^2}$, then potential energy equals $\dfrac{kq_1q_2}{r}$. Keep in mind that this may be negative. This is because if you have a positive and negative charge, the potential energy will be much greater when it's far away. The potential energy would be negative according to the formula, and it's more negative the closer the charges come together.

## Gauss's Law

MathJax TeX Test Page Gauss's Law is expressed as $$\Phi_E = \dfrac{q_{enc}}{\epsilon_0}$$ $\Phi_E$ is defined as electric field times area

Other times, it is seen as $\int E \cdot da = \dfrac{q_{enc}}{\epsilon_0}$, but the first expression is sufficient for the AP.

## Fields and Potentials of Other Charge Distributions

I am fairly sure this is referring to a uniform electric field. This means instead of extending radially, the field is created by two parallel plates, and it is uniform inside.

MathJax TeX Test Page Force equals $Eq$. This makes sense, because in our previous case, electric field = $\dfrac{kq}{r^2}$, which is the force divided by a charge. Electric potential energy equals $qEd$. This makes sense, because in our previous case, potential energy equals charge times electric potential (voltage), and voltage equals $Ed$.

# Conductors, Capacitors, Dielectrics

## Electrostatics with Conductors

A conductor is a material that allows the free flow of electrons. Electrostatic equilibrium means the charges are stable. It is important to know that a conductor in electrostatic equilibrium has no electric field.  This is due to Gauss's Law. If there were an electric field, then there must be charge inside. Because there is an electric field and charge inside, then those charges will move, but that means it's not in electrostatic equilibrium.

## Capacitors

Capacitors store charge. There are three main types

### Parallel Plate, Spherical, and Cylindrical

MathJax TeX Test Page The general equation for a capacitor is $$Q = CV$$ For a parallel plate capacitor, it's $$\dfrac{\epsilon_0 A}{d}$$ For a spherical capacitor, the capacitance is $$\dfrac{4\pi\epsilon_0}{\frac{1}{a} - \frac{1}{b}}$$ For a cylindrical capacitor, the capacitance is $$\dfrac{2\pi\epsilon_0L}{\ln(b/a)}$$
David Witten