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# Chapter 15: Electrostatics

Difficulty Level: At Grade Created by: CK-12

Most people have experienced some form of static electricity, but it is difficult to connect this to electricity that we use every day in the modern world.  In this chapter, we will study how electrical charges are split and transfered, the force that electrical charges exert on each other, and how that force can be expressed as an electric field.

Chapter Outline

### Chapter Summary

1. Electric charge is a conserved quantity that comes in two kinds: positive and negative.
2. Conductors are materials in which electrons can move freely, while insulators are materials in which electrons cannot move freely.
3. Coulomb’s law states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between the charge \begin{align*}F = k \frac{q_1 q_2}{r^2}\end{align*}, where \begin{align*}k\end{align*} is a constant of proportionality known as Coulomb’s constant.
4. The electric field \begin{align*}\vec{E}\end{align*}, at a point in space, is the quotient \begin{align*}\vec{E} = \frac{\vec{F}}{q}\end{align*}, where \begin{align*}q\end{align*} is a small positive test charge and \begin{align*}\vec{F}\end{align*} is the force experienced by that small positive test charge at the point in space where \begin{align*}E\end{align*} is measured.
5. The magnitude of the electric field \begin{align*}E\end{align*} due to a point charge \begin{align*}q\end{align*} at a distance \begin{align*}r\end{align*} from \begin{align*}q\end{align*} is \begin{align*}E = k \frac{q}{r^2}\end{align*}, where \begin{align*}k\end{align*} is a constant of proportionality known as Coulomb’s constant.
6. 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.
7. The potential energy of a charge \begin{align*}q\end{align*} at a point between two parallel-plate conductors is \begin{align*}PE=qEx\end{align*}, a reference point must be given such as \begin{align*}PE=0\end{align*} at \begin{align*}x=0\end{align*}.
8. A point charge \begin{align*}q\end{align*} has electric potential energy \begin{align*}PE_x\end{align*} and electric potential \begin{align*}V_x\end{align*} at point \begin{align*}x\end{align*}. Thus, \begin{align*}PE_x=qV_x\end{align*}
9. The word voltage is used when we mean potential difference.
10. It is common to write \begin{align*}V=Ed\end{align*}, where \begin{align*}V\end{align*} is understood to mean the voltage (or potential difference) between the plates of a parallel-plate conductor and \begin{align*}d\end{align*} is the distance between the plates.
11. The work done by the electric field in moving a charge between two parallel plate conductors is \begin{align*}W_{field}=-q \Delta V\end{align*}. The work done by an external force is \begin{align*}W_{external \ force}=q \Delta V\end{align*}.
12. Voltage can be thought of as the work per unit charge \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.

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Date Created:
Jan 13, 2016