Chapter 17
Electric Potential
Units of Chapter 17
• Electric Potential Energy and Potential
Difference
•Relation between Electric Potential and
Electric Field
•Equipotential Lines
•The Electron Volt, a Unit of Energy
•Electric Potential Due to Point Charges
•Potential Due to Electric Dipole; Dipole
Moment
Units of Chapter 17
• Capacitance
• Dielectrics
• Storage of Electric Energy
• Cathode Ray Tube: TV and Computer
Monitors, Oscilloscope
• The Electrocardiogram (ECG or EKG)
Objectives: The students will be able to:
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Distinguish between electric potential, electric potential
energy, and electric potential difference.
Draw the electric field pattern and equipotential line
pattern which exist between charged objects.
Determine the magnitude of the potential at a point a
known distance from a point charge or an arrangement
of point charges.
State the relationship between electric potential and
electric field and determine the potential difference
between two points a fixed distance apart in a region
where the electric field is uniform.
Electric Fields and WORK
In order to bring two like charges near each other work must be
done. In order to separate two opposite charges, work must be
done. Remember that whenever work gets done, energy
changes form.
As the monkey does work on the positive charge, he increases the energy of
that charge. The closer he brings it, the more electrical potential energy it
has. When he releases the charge, work gets done on the charge which
changes its energy from electrical potential energy to kinetic energy. Every
time he brings the charge back, he does work on the charge. If he brought
the charge closer to the other object, it would have more electrical potential
energy. If he brought 2 or 3 charges instead of one, then he would have had
to do more work so he would have created more electrical potential
energy. Electrical potential energy could be measured in Joules just like any
other form of energy.
Electric Fields and WORK
Consider a negative charge moving
in between 2 oppositely charged
parallel plates initial KE=0 Final
KE= 0, therefore in this case
Work = DPE
We call this ELECTRICAL potential
energy, UE, and it is equal to the
amount of work done by the
ELECTRIC FORCE, caused by the
ELECTRIC FIELD over distance, d,
which in this case is the plate
separation distance.
Is there a symbolic relationship with the FORMULA for gravitational
potential energy?
Electric Potential
U g  mgh
U g  U E (or W )
mq
gE
hxd
U E (W )  qEd
W
 Ed
q
Here we see the equation for gravitational
potential energy.
Instead of gravitational potential energy we are
talking about ELECTRIC POTENTIAL ENERGY
A charge will be in the field instead of a mass
The field will be an ELECTRIC FIELD instead of
a gravitational field
The displacement is the same in any reference
frame and use various symbols
Putting it all together!
Question: What does the LEFT side of the equation
mean in words? The amount of Energy per charge!
Change in electric potential energy
• For a positive test charge to be moved upward a
distance d, the electric force does negative work.
• The electric potential energy has increased and U is
positive (U2 > U1)
• If a negative charge is moved upward a distance d,
the electric force does positive work.
• The change in the electric potential energy U is
negative (U2 < U1)
Energy per charge
The amount of energy per charge has a specific
name and it is called, VOLTAGE or ELECTRIC
POTENTIAL (difference). Why the “difference”?
1 mv 2
W DK
DV 

 2
q
q
q
Video
Understanding “Difference”
Let’s say we have a proton placed
between a set of charged plates. If
the proton is held fixed at the
positive plate, the ELECTRIC
FIELD will apply a FORCE on the
proton (charge). Since like charges
repel, the proton is considered to
have a high potential (voltage)
similar to being above the ground.
It moves towards the negative plate
or low potential (voltage). The
plates are charged using a battery
source where one side is positive
and the other is negative. The
positive side is at 9V, for example,
and the negative side is at 0V. So
basically the charge travels through
a “change in voltage” much like a
falling mass experiences a
“change in height. (Note: The
electron does the opposite)
17.1 Electrostatic Potential Energy and
Potential Difference
The electrostatic force is
conservative – potential
energy can be defined
Change in electric potential
energy is negative of work
done by electric force:
(17-1)
17.1 Electrostatic Potential Energy and
Potential Difference
Electric potential is defined as potential
energy per unit charge:
(17-2a)
Unit of electric potential: the volt (V).
1 V = I J/C.
BEWARE!!!!!!
W is Electric Potential Energy (Joules)
is not
V is Electric Potential (Joules/Coulomb)
a.k.a Voltage, Potential Difference
The “other side” of that equation?
U g  mgh
U g  U E (or W )
mq
gE
hxd
U E (W )  qEd
W
 Ed
q
Since the amount of energy per charge is
called Electric Potential, or Voltage, the
product of the electric field and
displacement is also VOLTAGE
This makes sense as it is applied usually
to a set of PARALLEL PLATES.
DV=Ed
DV
E
d
17.1 Electrostatic Potential Energy and
Potential Difference
Only changes in potential can be measured,
allowing free assignment of V = 0.
(17-2b)
17.1 Electrostatic Potential Energy and
Potential Difference
Analogy between gravitational and electrical
potential energy:
The work done by an electric field to move a (+)
particle q from A to B is equal to the
negative change in potential energy.
Note: next slide shows the equation
17.2 Relation between Electric Potential
and Electric Field
Work is charge multiplied by potential:
Work is also force multiplied by
distance:
The work done by an electric field to move a (+) particle q from A to B is equal to the
.
negative change in potential energy
Electric Potential (V)
Electric potential is hard to understand, but easy
to measure.
• We commonly call it “voltage”, and its unit is
the Volt.
• 1 V = 1 J/C
• Electric potential is easily related to both the
electric potential energy, and to the electric
field.
• The change in potential energy is directly related to
the change in voltage.
DU = qDV
DV = DU/q
•
•
•
•
DU: change in electrical potential energy (J)
q: charge moved (C)
DV: potential difference (V)
All charges will spontaneously go to lower potential
energies if they are allowed to move.
Sample Problem: A 3.0 μC charge is moved through a
potential difference of 640 V. What is its potential
energy change?
Sample Problem: A 3.0 μC charge is moved through a
potential difference of 640 V. What is its potential
energy change?
17.2 Relation between Electric Potential
and Electric Field
Solving for the field,
Period 1 Start here
(17-4b)
If the field is not uniform, it can be
calculated at multiple points:
• Sample Problem: An electric field is parallel to the
x-axis. What is its magnitude and direction if the
potential difference between x =1.0 m and
x = 2.5 m is found to be +900 V?
• Sample Problem: An electric field is parallel to the
x-axis. What is its magnitude and direction if the
potential difference between x =1.0 m and
x = 2.5 m is found to be +900 V?
Sample Problem
Period 5
starts here
Sample Problem: If a proton is accelerated through a
potential difference of 2.000 V, what is its change
in potential energy?
How fast will this proton be moving if it started at
rest?
Q1 is -3uC
Q2 is 2uC
Q3 is 4uC
Skip right now
Sample Problem
How much work was done in assembling the charge configuration
shown below?
y (m)
2.0
-3 C
1.0
2 C
4 C
1.0
2.0
x (m)
17.3 Equipotential Lines
An equipotential is a line or
surface over which the
potential is constant.
Electric field lines are
perpendicular to
equipotentials.
The surface of a conductor is
an equipotential.
Lines that represent the electric potential. Any point
along a surface these lines must be perpendicular to
the electric field.
17.3 Equipotential Lines
Field lines are in red and equipotential lines are in green.
Figure 17-8
Topographic map
Contour lines are essentially gravitational equipotential lines.
Electric Field and Electric
Potential
E=-V/d
Two things about E and V:
• The electric field points in the direction of
decreasing electric potential.
• The electric field is always perpendicular to the
equipotential surface.
Equipotential Surfaces and the
Electric Field
An ideal conductor is an equipotential surface. Therefore, if
two conductors are at the same potential, the one that is
more curved will have a larger electric field around it. This is
also true for different parts of the same conductor.
Equipotential Surfaces and the
Electric Field
There are electric fields inside the human body; the
body is not a perfect conductor, so there are also
potential differences.
An electrocardiograph
plots the heart’s
electrical activity.
Cardiac Cycle
Electrical
System of the
Heart
Equipotential Surfaces and the
Electric Field
An electroencephalograph measures
the electrical activity of the brain:
17.4 The Electron Volt, a Unit of Energy
One electron volt (eV) is the energy gained by
an electron moving through a potential
difference of one volt.
Practice Problem 1: page 489 #2
Practice Problem 1: page 489 #2
Practice Problem 2: page 489 #5
How strong is the electric field between two parallel
plates 5.8 mm apart if the potential difference between
them is 220 V?
Practice Problem 2: page 489 #5
How strong is the electric field between two parallel
plates 5.8 mm apart if the potential difference between
them is 220 V?
pHET activity – Exploring Electric Potential,
Electric Field and Distance Relationships
Note: When finished go to
http://vnatsci.ltu.edu/s_schneider/physlets/main/equipotentials.shtml
and experiment with the various charge configurations.
(written on hand-out)
Homework
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Complete computer activity responses.
P.488 Questions #1, 2, 3
P. 489 Problems # 1, 3, 6, 7, 9
Question 1 answer
Question 2 Answer
Question 3 Answer
Closure
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Kahoot