<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />

# Chapter 16: Electric Potential

Difficulty Level: At Grade Created by: CK-12

If there is a strong enough electric field, sparks form in the air where the electricity jumps from one object to another.  In this chapter, we discuss electrical energy and electric potential.

Chapter Outline

### Chapter Summary

1. The electric field between two parallel-plate conductors is considered uniform far away from the plate edges if the size of the plates is large compared to their separation distance.
2. The potential energy of a charge q\begin{align*}q\end{align*} at a point between two parallel-plate conductors is PE=qEx\begin{align*}PE=qEx\end{align*}, a reference point must be given such as PE=0\begin{align*}PE=0\end{align*} at x=0\begin{align*}x=0\end{align*}.
3. A point charge q\begin{align*}q\end{align*} has electric potential energy PEx\begin{align*}PE_x\end{align*} and electric potential Vx\begin{align*}V_x\end{align*} at point x\begin{align*}x\end{align*}. Thus, PEx=qVx\begin{align*}PE_x=qV_x\end{align*}
4. The word voltage is used when we mean potential difference.
5. It is common to write V=Ed\begin{align*}V=Ed\end{align*}, where V\begin{align*}V\end{align*} is understood to mean the voltage (or potential difference) between the plates of a parallel-plate conductor and d\begin{align*}d\end{align*} is the distance between the plates.
6. The work done by the electric field in moving a charge between two parallel plate conductors is Wfield=qΔV\begin{align*}W_{field}=-q \Delta V\end{align*}. The work done by an external force is Wexternal force=qΔV\begin{align*}W_{external \ force}=q \Delta V\end{align*}.
7. Voltage can be thought of as the work per unit charge V=Wq\begin{align*}V=\frac{W}{q}\end{align*}; that is, how much work is required per unit charge to move a charged particle in an electric field.
8. Capacitance of an air-gap capacitor is given by C=ε0Ad\begin{align*}C = \varepsilon_0 \frac{A}{d}\end{align*} where A\begin{align*}A\end{align*} is the area of the capacitor and d\begin{align*}d\end{align*} is the separation distance between the plates.
9. The charge on a capacitor is directly proportional to the voltage of the capacitor Q=CV\begin{align*}Q = CV\end{align*}.
10. A dielectric material placed between the plates increases the capacitance of the capacitor. The capacitance of a capacitor with a dielectric is expressed as C=kε0Ad\begin{align*}C = k\varepsilon_0 \frac{A}{d}\end{align*}, where k\begin{align*}k\end{align*} is the dielectric constant.
11. The energy stored in a capacitor can be expressed as

UUU=12QV=12QV2=12Q2C\begin{align*}U & = \frac{1}{2}QV\\ U & = \frac{1}{2}QV^2\\ U & = \frac{1}{2} \frac{Q^2}{C}\end{align*}
Where Q\begin{align*}Q\end{align*} is the charge on the capacitor and V\begin{align*}V\end{align*} is the voltage of the capacitor.

Show Hide Details
Description
Difficulty Level:
Authors:
Editors:
Tags:
Subjects:
Date Created:
Jan 13, 2016