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Chapter 18 – Part I -Potential
Things to remember
 Definition of WORK
 W=F d cos(q)
 Definition of Potential Energy
 Work necessary to bring an
object from some reference
level to the final position.
 For the diagram
 PE=Mgh
M
Picture a Region of
space Where there is an Electric Field
 Imagine there is a particle of charge q at some location.
 Imagine that the particle must be moved to another spot within
the field.
 Work must be done in order to accomplish this.
What (or who) must do this work?
An external agent (person)
B. The Field itself
C. Either of the above
D. Dr. Bindell
A.
What we will do ….
E
+
charge
Mrs. Fields
Mr. External
 For the moment, assume the charge has MASS. (It may not.)
 Assume the charge is initially stationary.
 The charge is to be moved to the left.
 The charge is to be moved at CONSTANT velocity.
During this process, who is pushing?
A. Mr. External
B. Mrs. Fields
C. Dr. Bindell
E
+
charge
Mrs. Fields
Mr. External
When we start the process, the charge
that is stationary must be brought up to
speed.
A. This is work and must be accounted for.
This is work but we don’t have to worry
about it.
C. Only Dr. Bindell worries about stupid stuff
like this!
B.
About the work that they do ..
A. Mrs. Fields does more work than Mr. External.
B. Mr. External does more work than Mrs. Fields.
C. Both do the same amount of work.
D. Each does the negative amount of work than
the other does.
Start and Sop
 ENERGY is required to bring the charge up to speed (if it has
mass).
 ENERGY is required to bring the particle back to rest (if it has
mass).
 The sum of these two is ZERO.
So, when we move a charge in an Electric
Field ..
 Move the charge at constant velocity so it is in mechanical
equilibrium all the time.
 Ignore the acceleration at the beginning because you have to do
the same amount of negative work to stop it when you get there.
Summary- When an object is moved from one point to another in an
Electric Field,
 It takes energy (work) to move it.
 This work can be done by an external force (you).
 You can also think of this as the
FIELD
negative
doing the
of this amount of work on the particle.
And also remember:
The net work done by a conservative (field)
force on a particle moving
around a closed path is
ZERO!
Huh? What does this mean??
A nice landscape
Work done by external force = mgh
How much work here by
gravitational field?
h

mg
The gravitational case:

Someone else’s path

IMPORTANT (For a conservative field)
 The work necessary for an external agent to
move a charge from an initial point to a final
point is INDEPENDENT OF THE PATH
CHOSEN!
The Electric Field

Is a conservative field.

No frictional losses, etc.
Is created by charges.
When one (external agent) moves a test
charge from one point in a field to
another, the external agent must do
work.
 This work is equal to the increase in
potential energy of the charge.
 It is also the NEGATIVE of the work
done BY THE FIELD in moving the
charge from the same points.


A few things to remember…
 A conservative force is NOT a Republican.
 An External Agent is NOT 007.
Definition – Potential Energy
 PE or U is the work done by an external agent in moving a
charge from a REFERENCE POSITION to a different
position.
 A Reference ZERO is placed at the most convenient position
 Like the ground level in many gravitational potential energy
problems.
Example:
Work by External Agent
Wexternal = F  d = qEd= U
E
d
Zero Level
q
F
Work done by the Field
is:
Wfield= -qEd
= -Wexternal
A uniform electric field of magnitude 290 V/m is directed in the
positive x direction. A +13.0 µC charge moves from the origin to the
point (x, y) = (20.0 cm, 50.0 cm).(a) What is the change in the
potential energy of the charge field system?
[-0.000754] J
YOU
Think about YOU being the external agent and
you are therefore doing the work.
Parallel Sheets of Charge
Parallel Sheets of Charge II
Get to Work
+
+
q’
q
IMPORTANT RESULT
The potential energy U of a system consisting of two charges
q and q’ separated by a distance r Is given by:
qq'
U k
r
This also applies to multiple charges.
What is the Potential Energy of q’?
q3 q'
q1q'
q2 q '
U k
k
k
r1
r2
r3
Unit is JOULES
AN IMPORTANT DEFINITION
 Just as the ELECTRIC FIELD was defined as the FORCE per
UNIT CHARGE:
F
E
q
VECTOR
We define ELECTRICAL POTENTIAL as the POTENTIAL
ENERGY PER UNIT CHARGE:
U
V
q
SCALAR
UNITS OF POTENTIAL
U
Joules
V 
 VOLT
q Coulomb
Furthermore…
U Wapplied
V 

q
q
so
Wapplied  qV
If we move a particle through a potential
difference of V, the work from an external
“person” necessary to do this is qV
Example
Electric Field = 2 N/C

1 mC
d= 100 meters
Work done by EXTERNAL agent
 Change in potential Energy.
PE  qEd  1mC  2( N / C ) 100m
 2 10  4 Joules
One Step More
Work done by EXTERNAL agent
 Change in potential Energy.
PE  qEd  1mC  2( N / C ) 100m
 2 10  4 Joules
PE
Change in POTENTIAL 
q
2 104 Joules
J
V 
 200  200 Volts
6
110 C
C
Consider Two Plates
OOPS!
The difference in potential between the
accelerating plates in the electron gun of a
TV picture tube is about 25 000 V. If the
distance between these plates is 1.50 cm,
what is the magnitude of the uniform
electric field in this region?
Important
 We defined an absolute level of potential.
 To do this, we needed to define a REFERENCE or ZERO
level for potential.
 For a uniform field, it didn’t matter where we placed the
reference.
 For POINT CHARGES, we will see shortly that we must
place the level at infinity or the math gets very messy!
An Equipotential Surface is defined
as a surface on which the potential is
constant.
V  0
It takes NO work to move a charged particle
between two points at the same potential.
The locus of all possible points that require NO
WORK to move the charge to is actually a surface.
Example: A Set of Equipotenital
Surfaces
Example
What is the Potential Energy of q’?
q3 q'
q1q'
q2 q '
U k 2 k 2 k 2
r1
r2
r3
Unit is JOULES
q3
U
q1
q2
V  k 2 k 2 k 2
q'
r1
r2
r3
Units are VOLTS
Imagine a 1 Coulomb charge at each point.
How much work did it take to create this
Charged triangle??