Text book
Physics; John D. Cutnell and Kenneth W.
Johnson; 7th edition; Wiley; 2007.
Electric Potential Energy and
the Electric Potential
The upper surface of this car is covered by solar cells. Sunlight penetrates the cells and
provides the energy that separates positive and negative charges in the materials from which
the cells are made. Thus, each cell develops positive and negative terminals, much like the
terminals of a battery and, in effect, converts solar energy into the electric energy that powers
the car. Electric potential energy and the related concept of electric potential are the subjects of
this chapter. (© AP/Wide World Photos)

The work WAB done by
the gravitational force
when the ball falls
from a height hA to a
height hB is:
WAB = mghA – mghB =
GPEA - GPEB

The work WAB done by
the electric force
equals the difference
between the electric
potential EPE at A and
that at B:
WAB = EPEA - EPEB
Definition of Electric Potential V:
The electric potential V at a given point is the electric
potential energy EPE of a small test charge q0 situated
at that point divided by the charge itself:

V = EPE/q0
SI Unit of Electric Potential:
joule/coulomb = volt (V)
The potential difference between two points A and B is
given by:
EPEB EPEA  WAB
VB  VA 


q0
q0
q0
Where WAB is the work done by the electric force when
a charge q0 moves from A to B.
OR
 EPE   WAB
V 

q0
q0
If the work done by the electric force as the test charge
(q0 = +2.0 x 10-6 C) moves from A to B is WAB = + 5.0 x
10-5 J. (a) Find the value of the difference, (EPE) =
EPEB - EPEA, in the electric potential energies of the
charge between these points. (b) Determine the
potential difference, V = VB - VA, between the points.
Answer:
a)
(EPE) = EPEB – EPEA= -WAB = - 5.0 x 10-5 J
b)
V = VB – VA = - 5.0 x 10-5 J/ +2.0 x 10-6 C = -25 V
A particle has a mass of 1.8 x 10-5 kg and a charge of +3.0 x
10-5 C. It is released from rest at point A and accelerates
until it reaches point B, as in figure (a). The particle moves
on a horizontal straight line and does not rotate. The only
forces acting on the particle are the gravitational force and
an electrostatic force. The electric potential at A is 25 V
greater than that at B; in other words, VA – VB = 25V. What
is the translational speed of the particle at point B?
1
1
1 2
2
2
E  m v  I   m g h  k x  EPE

 2
2
2
Electric
  Gravitational  potential
Translational
kinetic
energy
Rotational
kinetic
energy
potential
energy
Elastic
potential
energy
energy
1
1 2
2
I  k x  0
2
2
1
1
2
2
m v A  m g hA  EPEA  m vB  m g hB  EPEB
2
2
1
1
2
2
m v A  EPEA  m vB  EPEB
2
2
2 EPEA  EPEB 
vB  v 
m
2
A
Since EPEA – EPEB = q0 (VA – VB)
2 q0 VA VB 
vB  v 
m
2
A


5
2


3
.
0

10
C 25V 
2
vB  0 
 9.1 m / s
5
1.8 10 kg
Capacitor consists of two conductors of any
shape placed near one another without touching
Dielectric is the electrically insulated
material filled in the region between
the conductors or plates.
The magnitude q of the charge on each plate of a
capacitor is directly proportional to the magnitude V
of the potential difference between the plates:
q=CV
where C is the capacitance.
SI Unit of Capacitance: coulomb/volt = farad (F)
The ability of a capacitor to store charge lies at the
heart of the random-access memory (RAM) chips
used in computers, where information is stored in the
form of the “ones” and “zeros” that comprise binary
numbers. A single RAM chip often contains millions
of such transistor–capacitor units.
A charged capacitor means that a “one” has been
stored, whereas an uncharged capacitor means that a
“zero” has been stored.
During a heart attack, the heart produces a rapid, unregulated
pattern of beats, a condition known as cardiac fibrillation.
Cardiac fibrillation can often be stopped by sending a very fast
discharge of electrical energy through the heart. Emergency
medical personnel use defibrillators. A paddle is connected to
each plate of a large capacitor, and the paddles are placed on the
chest near the heart. The capacitor is charged to a potential
difference of about a thousand volts. The
capacitor is then discharged in a few
thousandths of a second; the discharge current
passes through a paddle, the heart, and the
other paddle. Within a few seconds, the heart
often returns to its normal beating pattern.
Figure (a) The electric field lines inside
an empty capacitor. (b) The electric field
produced by the charges on the plates
aligns the molecular dipoles within the
dielectric end to end. (c) The surface
charges on the dielectric reduce the
electric field inside the dielectric. The
space between the dielectric and the
plates is added for clarity. In reality, the
dielectric fills the region between the
plates.
Substance
Dielectric
Constant, κ
Vacuum
1
Air
1.000 54
Teflon
2.1
Benzene
2.28
Paper (royal gray)
3.3
Ruby mica
5.4
Neoprene rubber
6.7
Methyl alcohol
33.6
Water
80.4
E0
The field E0 without the dielectric is

E
greater than the field E inside the dielectric.
C
 o A
d
Where:
C is the capacitance.
 is the dielectric constant.
 o is the permittivity of free space.
A is the area of the plate.
d is the distance between the plates.
Each key is mounted on one end of a plunger, the other end being
attached to a movable metal plate. The movable plate is separated
from a fixed plate, the two plates forming a capacitor. When the key is
pressed, the movable plate is pushed closer to the fixed plate, and the
capacitance increases.
Electronic circuitry enables the computer to detect the
change in capacitance, thereby recognizing which key
has been pressed. The separation of the plates is
normally 5.00 x 10-3 m but decreases to 0.150 x 10-3 m
when a key is pressed. The plate area is 9.50 x 10-5 m2,
and the capacitor is filled with a material whose
dielectric constant is 3.50. Determine the change in
capacitance that is detected by the computer.
Answer:
  0 A 3.50 8.85 10 12 C 2 N  m 2 9.50 10 5 m 2 
C
d

C 19.6 10 12 F 19.6 pF
0.150 10 3 m
When a capacitor stores charge, it also stores
energy.
1
Energy  q V
2
1
Energy  C V 2
2
q2
Energy 
2C
Conduction of Electrical Signals in Neurons
The human nervous system is remarkable for its
ability to transmit information in the form
of electrical signals. These signals are
carried by the nerves, and the concept of
electric potential
difference plays an
important role in the
process.

Several important medical diagnostic techniques depend on
the fact that the surface of the human body is not an equipotential surface. Between various points on the body there
are small potential differences (approximately 30 – 500
μV), which provide the basis for electrocardiography,
electroencephalography, and electroretinography. The
potential differences can be traced to the electrical
characteristics of muscle cells and nerve cells. In carrying
out their biological functions, these cells utilize positively
charged sodium and potassium ions and negatively charged
chlorine ions that exist within the cells and in the
extracellular fluid. As a result of such charged particles,
electric fields are generated that extend to the surface of the
body and lead to small potential differences.
The figure shows some locations on the body where
electrodes are placed to measure potential differences in
electrocardiography. The potential difference between two
locations changes as the heart beats and forms a repetitive
pattern. The recorded pattern of potential difference versus
time is called an electrocardiogram, and its shape depends
on which pair of points in the picture is used to locate the
electrodes.
The distinct differences between the healthy
(normal) and damaged (abnormal) hearts
provide physicians with a valuable
diagnostic tool.
In electroencephalography the electrodes are placed at
specific locations on the head, and they
record the potential differences that
characterize brain behavior. The graph
of potential difference versus time is known as an
electroencephalogram (EEG). The various parts of the
patterns in an EEG are often referred to as “waves” or
“rhythms.” The drawing shows an example of the main
resting rhythm of the brain, the so-called alpha rhythm, and
also illustrates the distinct differences that
are found between the EEGs generated by
healthy (normal) and diseased (abnormal)
tissue.
The electrical characteristics of the retina of the eye lead to the
potential differences measured in
electroretinography. The figure shows a
typical electrode placement used to record
the pattern of potential difference versus time that occurs when
the eye is stimulated by a flash of light. One electrode is
mounted on a contact lens, while the other is often placed on
the forehead. The recorded pattern is called an
electroretinogram (ERG), parts of the pattern being referred to
as the “A wave” and the “B wave.” As the
graphs show, the ERGs of normal and
diseased (abnormal) eyes can differ
markedly.
1/2156) Suppose that the electric potential outside a living
cell is higher than that inside the cell by 0.070 V. How much
work is done by the electric force when a sodium ion
(charge = +e) moves from the outside to the inside?
1.1 x 10-20 J
3/2156) Point A is at a potential of +250 V, and point B is at
a potential of −150 V. An α-particle is a helium nucleus that
contains two protons and two neutrons; the neutrons are
electrically neutral. An α-particle starts from rest at A and
accelerates toward B. When the α-particle arrives at B, what
kinetic energy (in electron volts) does it have?
8.0 x 102 eV
36/2162) An axon is the relatively long tail-like part of a
neuron, or nerve cell. The outer surface of the axon
membrane (dielectric constant = 5, thickness = 1 x 10-8 m)
is charged positively, and the inner portion is charged
negatively. Thus, the membrane is a kind of capacitor.
Assuming that an axon can be treated like a parallel plate
capacitor with a plate area of 5 x 10-6 m2, what is its
capacitance?
37/2162) The membrane that surrounds a certain type of
living cell has a surface area of 5.0 x 10-9 m2 and a
thickness of 1.0 x 10-8 m. Assume that the membrane
behaves like a parallel plate capacitor and has a dielectric
constant of 5.0. (a) The potential on the outer surface of the
membrane is +60.0 mV greater than that on the inside
surface. How much charge resides on the outer surface? (b)
If the charge in part (a) is due to K+ ions (charge +e), how
many such ions are present on the outer surface?
1.3 x 10-12 C, 8.3 x 106
38/2162) What voltage is required to store 7.2 x 10-5 C of
charge on the plates of a 6.0 μF capacitor?