Sections

Section Summary
# Section Summary

### 2.1 Electric Potential Energy: Potential Difference

- Electric potential is potential energy per unit charge.
- The potential difference between points A and B, ${V}_{\mathrm{B}}\u2013{V}_{\mathrm{A}}\text{,}$ defined to be the change in potential energy of a charge
*$q$*moved from A to B, is equal to the change in potential energy divided by the charge, Potential difference is commonly called voltage, represented by the symbol $\text{\Delta}V\text{.}$$$\mathrm{\Delta}V=\frac{\text{\Delta PE}}{q}\phantom{\rule{0.25em}{0ex}}\text{and \Delta PE =}\phantom{\rule{0.25em}{0ex}}q\mathrm{\Delta}V$$ - An electron volt is the energy given to a fundamental charge accelerated through a potential difference of 1 V. In equation form
$$\begin{array}{lll}\text{1 eV}& =& \left(1.60\phantom{\rule{0.25em}{0ex}}\times \phantom{\rule{0.25em}{0ex}}{\text{10}}^{\text{\u201319}}\phantom{\rule{0.25em}{0ex}}\text{C}\right)\left(\mathrm{1\; V}\right)=\left(1.60\phantom{\rule{0.25em}{0ex}}\times \phantom{\rule{0.25em}{0ex}}{\text{10}}^{\text{\u201319}}\phantom{\rule{0.25em}{0ex}}\text{C}\right)\left(\mathrm{1\; J/C}\right)\\ & =& 1.60\phantom{\rule{0.25em}{0ex}}\times \phantom{\rule{0.25em}{0ex}}{\text{10}}^{\text{\u201319}}\phantom{\rule{0.25em}{0ex}}\text{J.}\end{array}$$
- Mechanical energy is the sum of the kinetic energy and potential energy of a system, that is, $\text{KE}+\text{PE}.$ This sum is a constant.

### 2.2 Electric Potential in a Uniform Electric Field

- The voltage between points A and B is
$$\begin{array}{c}\left.\begin{array}{c}{V}_{\text{AB}}=\mathrm{Ed}\\ E=\frac{{V}_{\text{AB}}}{d}\end{array}\right\}\text{(uniform}\phantom{\rule{0.25em}{0ex}}E\phantom{\rule{0.25em}{0ex}}\text{- field only),}\end{array}$$where $d$ is the distance from A to B, or the distance between the plates.
- In equation form, the general relationship between voltage and electric field is
$$E=\phantom{\rule{0.25em}{0ex}}\u2013\frac{\mathrm{\Delta}V}{\mathrm{\Delta}s},$$where $\mathrm{\Delta}s$ is the distance over which the change in potential, $\mathrm{\Delta}V\text{,}$ takes place. The minus sign tells us that $\mathbf{\text{E}}$ points in the direction of decreasing potential. The electric field is said to be the
—as in grade or slope—of the electric potential.*gradient*

### 2.3 Electrical Potential Due to a Point Charge

- Electric potential of a point charge is $V=\text{kQ}/r\text{.}$
- Electric potential is a scalar, and electric field is a vector. Addition of voltages as numbers gives the voltage due to a combination of point charges, whereas addition of individual fields as vectors gives the total electric field.

### 2.4 Equipotential Lines

- An equipotential line is a line along which the electric potential is constant.
- An equipotential surface is a three-dimensional version of equipotential lines.
- Equipotential lines are always perpendicular to electric field lines.
- The process by which a conductor can be fixed at zero volts by connecting it to Earth with a good conductor is called grounding.

### 2.5 Capacitors and Dielectrics

- A capacitor is a device used to store charge.
- The amount of charge $Q$ a capacitor can store depends on two major factors—the voltage applied and the capacitor’s physical characteristics, such as its size.
- The capacitance $C$ is the amount of charge stored per volt
*,*or$$C=\frac{Q}{V}.$$ - The capacitance of a parallel plate capacitor is $C={\epsilon}_{0}\phantom{\rule{0.15em}{0ex}}\frac{A}{d}\text{,}$ when the plates are separated by air or free space. ${\epsilon}_{\text{0}}\phantom{\rule{0.25em}{0ex}}$ is called the permittivity of free space.
- A parallel plate capacitor with a dielectric between its plates has a capacitance given by
$$C={\mathrm{\kappa \epsilon}}_{0}\phantom{\rule{0.25em}{0ex}}\frac{A}{d},$$where $\kappa $ is the dielectric constant of the material.
- The maximum electric field strength above which an insulating material begins to break down and conduct is called dielectric strength.

### 2.6 Capacitors in Series and Parallel

- Total capacitance in series $\frac{1}{{C}_{\text{S}}}=\frac{1}{{C}_{1}}+\frac{1}{{C}_{2}}+\frac{1}{{C}_{3}}+\text{.}\text{.}\text{.}$
- Total capacitance in parallel ${C}_{\text{p}}={C}_{1}+{C}_{2}+{C}_{3}+\text{.}\text{.}\text{.}$
- If a circuit contains a combination of capacitors in series and parallel, identify series and parallel parts, compute their capacitances, and then find the total.

### 2.7 Energy Stored in Capacitors

- Capacitors are used in a variety of devices, including defibrillators, microelectronics such as calculators, and flash lamps, to supply energy.
- The energy stored in a capacitor can be expressed in three ways:
$${E}_{\text{cap}}=\frac{\text{QV}}{2}=\frac{{\text{CV}}^{2}}{2}=\frac{{Q}^{2}}{2C},$$where $Q$ is the charge, $V$ is the voltage, and $C$ is the capacitance of the capacitor. The energy is in joules when the charge is in coulombs, voltage is in volts, and capacitance is in farads.