Electric Potential & Capacitor Energy Cheat Sheet

Key Facts

• Electric potential is electric potential energy per unit charge, written as $V = \frac{U}{q}$.
• Electric potential difference is the change in potential energy per unit charge, written as $\Delta V = \frac{\Delta U}{q}$.
• The electric potential from a point charge is $V = \frac{kQ}{r}$, where $k = 8.99 \times 10^9\ \text{N}\cdot\text{m}^2/\text{C}^2$.
• Electric potential energy for two point charges is $U = \frac{kq_1q_2}{r}$.
• In a uniform electric field, the potential difference over distance $d$ along the field is $\Delta V = -Ed$.
• Capacitance is the charge stored per volt, written as $C = \frac{Q}{\Delta V}$.
• The energy stored in a capacitor can be calculated using $U = \frac{1}{2}C(\Delta V)^2$, $U = \frac{1}{2}Q\Delta V$, or $U = \frac{Q^2}{2C}$.
• For a parallel-plate capacitor, $C = \frac{\varepsilon A}{d}$, where $A$ is plate area, $d$ is separation, and $\varepsilon$ is the permittivity of the material between plates.

Vocabulary

Electric Potential

Electric potential is the electric potential energy per unit charge at a location, measured in volts.

Potential Difference

Potential difference is the change in electric potential between two points, written as $\Delta V$.

Electric Potential Energy

Electric potential energy is the energy a charge has because of its position in an electric field.

Capacitance

Capacitance is a measure of how much charge a capacitor stores for each volt of potential difference.

Capacitor

A capacitor is a device that stores separated charge and electric energy between conductors.

Permittivity

Permittivity is a material property that affects how strongly an electric field forms inside a material.