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# 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 $q$ at a point between two parallel-plate conductors is $PE=qEx$, a reference point must be given such as $PE=0$ at $x=0$.
3. A point charge $q$ has electric potential energy $PE_x$ and electric potential $V_x$ at point $x$. Thus, $PE_x=qV_x$
4. The word voltage is used when we mean potential difference.
5. It is common to write $V=Ed$, where $V$ is understood to mean the voltage (or potential difference) between the plates of a parallel-plate conductor and $d$ is the distance between the plates.
6. The work done by the electric field in moving a charge between two parallel plate conductors is $W_{field}=-q \Delta V$. The work done by an external force is $W_{external \ force}=q \Delta V$.
7. Voltage can be thought of as the work per unit charge $V=\frac{W}{q}$; 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 $C = \varepsilon_0 \frac{A}{d}$ where $A$ is the area of the capacitor and $d$ is the separation distance between the plates.
9. The charge on a capacitor is directly proportional to the voltage of the capacitor $Q = CV$.
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 $C = k\varepsilon_0 \frac{A}{d}$, where $k$ is the dielectric constant.
11. The energy stored in a capacitor can be expressed as

$U & = \frac{1}{2}QV\\U & = \frac{1}{2}QV^2\\U & = \frac{1}{2} \frac{Q^2}{C}$
Where $Q$ is the charge on the capacitor and $V$ is the voltage of the capacitor.

Jun 27, 2013