19.1 Electric Potential Energy: Potential Difference

Electric potential is potential energy per unit charge.
The potential difference between points A and B, $V_{B} - V_{A}$ , 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 $Δ V$ .
$Δ V = \frac{ΔPE}{q} and ΔPE = q Δ V .$
An electron volt is the energy given to a fundamental charge accelerated through a potential difference of 1 V. In equation form,
$\begin{array}{l} 1 eV & = & (1.60 \times 10^{–19} C) (1 V) = \\ (1.60 \times 10^{–19} C) (1 J/C) \\ = & 1.60 \times 10^{–19} J. \end{array}$
Mechanical energy is the sum of the kinetic energy and potential energy of a system, that is, $KE + PE .$ This sum is a constant.

19.2 Electric Potential in a Uniform Electric Field

The voltage between points A and B is
$\begin{matrix} \begin{matrix} V_{AB} = Ed \\ E = \frac{V_{AB}}{d} \end{matrix}\} (uniform E - field only), \end{matrix}$
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
$E = - \frac{Δ V}{Δ s},$
where $Δ s$ is the distance over which the change in potential, $Δ V$ , takes place. The minus sign tells us that $E$ points in the direction of decreasing potential.) The electric field is said to be the gradient (as in grade or slope) of the electric potential.

Electric potential of a point charge is $V = kQ / r$ .
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.

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 the earth with a good conductor is called grounding.

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 $C = ε_{0} \frac{A}{d}$ , when the plates are separated by air or free space. $ε_{0}$ is called the permittivity of free space.
A parallel plate capacitor with a dielectric between its plates has a capacitance given by
$C = {κε}_{0} \frac{A}{d},$
where $κ$ 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.

Total capacitance in series $\frac{1}{C_{S}} = \frac{1}{C_{1}} + \frac{1}{C_{2}} + \frac{1}{C_{3}} + . . .$
Total capacitance in parallel $C_{p} = C_{1} + C_{2} + C_{3} + . . .$
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.

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:
$E_{cap} = \frac{QV}{2} = \frac{{CV}^{2}}{2} = \frac{Q^{2}}{2 C},$
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.