Download Chap22_PartII

How Do We Describe the Electric Field
Between Charged Parallel Plates?
Chapter 22: Coulomb’s Law and Electric
Fields Part II
OBJECTIVES
 To learn how work is done and potential energy is stored
in an electric field.
 Define and calculate electric potential difference.
 To describe the Electric field intensity between charged
parallel plates.
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When a Test charge is present in an Electric
Field, can it acquire Potential Energy?
Can it Acquire Kinetic Energy?
+
A
B
+
+
A charge at any point in an
electric field possesses potential
energy. Consider the electric field
of the positively charged sphere.
If we moved a small positive
charge +q from B to A, we have to
do WORK against the electric
field. If we were to “let go” of +q
at point A, it will accelerate to B
(and beyond) and gain KE
(1/2mv2). This KE is obtained at
the expense of the potential energy
(W =PE) possessed by +q when it
was at A.
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Electric Field & Work of a Small Charge
in an Electric Field
Consider the motion of the a positive test charge within the
electric field created by a positive source charge.
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Electric Field & Work of a Small Charge
in an Electric Field
Now we will consider the motion of the same positive test
charge within the electric field created by a negative source
charge.
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Electric Fields, Work & Electric
Potential Energy
Complete the following statement:
When work is done on a
positive test charge by an
external force to move it from
one location to another,
potential energy _________
(increases, decreases).
When work is done on a positive test charge to move it from
one location to another, potential energy increases.
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Electric Fields, Work & Electric
Potential Energy
The following diagrams show an electric field (represented by arrows) and two
points - labeled A and B - located within the electric field. A positive test charge is
shown at point A. For each diagram, indicate whether work must be done upon
the charge to move it from point A to point B. Finally, indicate the point (A or B)
with the greatest electric potential energy
Work done on charge? Yes or No
Electric PE is greatest at: A B
Work done on charge? Yes or No
Electric PE is greatest at: A B
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Electric Fields, Work & Electric
Potential Energy
2. The following diagrams show an electric field (represented by arrows) and two
points - labeled A and B - located within the electric field. A positive test charge is
shown at point A. For each diagram, indicate whether work must be done upon
the charge to move it from point A to point B. Finally, indicate the point (A or B)
with the greatest electric potential energy.
Work done on charge? Yes or No
Electric PE is greatest at: A B
Work done on charge? Yes or No
Electric PE is greatest at: A B
How are these field lines different from the field
lines of slide #3?
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Uniform Electric Force & Electric Field
A uniform electric force and field can be made by placing
two large conducting plates parallel to each other. One is
charged positively and the other negatively. The electric
field between the plates is constant except for the edges of
the plates.
Remember the
equation: E=F/q. If E is
fixed for a charge q,
then F must be fixed
(uniform) within the
plates!
Internet Link: What are Equipotential Lines?
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Electrical Potential Energy Within a
Uniform Field
 Supposed a positive test charge is “pushed” from
point b to point a.
 The work done on the particle is W
= Fd or qEd
 When dealing with electrical charges, we like to call
this type of energy:
ELECTRICAL
POTENTIAL ENERGY
Question: Is there a symbolic relationship with the
FORMULA for gravitational potential energy?
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Electrical Potential Energy vs.
Gravitational Potential Energy
U g  mgh
Here we see the equation for gravitational potential
energy, Ug.
of gravitational potential energy we are
U g  U E (or W ) Instead
talking about ELECTRIC POTENTIAL ENERGY
mq
A charge will be in the field instead of a mass
gE
The field will be an ELECTRIC FIELD instead of a
gravitational field
hxd
U E (W )  qEd
W
 Ed
q
The displacement is the same in any reference
frame and use various symbols
Note the UE (W) is the Electrical Potential Energy
Question: If you divided both sides of the equation by q,
then what does the LEFT side of the equation mean in
words?
The amount of Energy per charge(J/C)!
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Electrical Potential Energy Per Charge
The amount of energy per charge has a specific name
and it is called, VOLTAGE or ELECTRIC
POTENTIAL (difference).
W
V
q
We can therefore write:
W  qV
Why do we use the word “difference”?
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Understanding Electric Potential
“Difference” For a Charge in an EField.
The difference of potential between
two points is defined as the
work it takes to move a unit positive charge from the point of lower
potential (B) to that at higher potential (A).
PE W
V  Vb  Va 

q
q
In this formula, V is the electric potential difference, PE is the
electric potential energy between point b and point a, W is work,
and q is the magnitude of the test charge. The SI unit of electric
potential difference is Joule/Coulomb or volt (V).
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Understanding Electric Potential
“Difference” For Charged Plates
Notice the electric field lines
at the edges!
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. Just like a mass
accelerates as it falls, so does the charge
in a field of parallel plates. (Note: The
electron does the opposite)
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Electric Potential Energy vs. Electric
Potential
W is Electric Potential Energy (Joules)
is not
V is Electric Potential (Joules/Coulomb)
a.k.a Voltage, Potential Difference
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Units of Electric Potential
The quantity electric potential is defined as the amount of _____.
a. electric potential energy
b. force acting upon a charge
c. potential energy per charge
d. force per charge
Answer: C
Electric potential is the amount of potential energy per unit of charge.
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What about the “other side” of the
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.
V=Ed
V
E
d
Notice the electric field lines
at the edges!
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Review of some Important facts Concerning
The Electric Field around Parallel Plates
 The work done by the electric field E to
move a positive charge q from A to B is
W = qV
 Using W =Fd and F = qE, the potential
difference for a charged parallel plate
conductor is V = Ed
 If the potential difference (V) is fixed, the
electric field strength (E) is the same (as
well as the force (F) on the charge) at
any point between the parallel plates.
 Internet Link: RegentsPrep.org**
+
d
**Very important!!!
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Electric Potential Energy (Work)
Between Two Charges
Sample Problem
It takes 5.0 x 10-3 J of work to move a
positive test charge of 2.5 x 10-4C from
point X to point Y on an electric field.
What is the difference of Potential
between X and Y?
Solution
Work = qV
W= 5.0 x 10-3 J
q = +2.5 x 10-4C
V= W/q = 5.0 x 10-3J/2.5 x 10-4C = 20 J/C = 20 volts
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Relation between Electric Potential and
Electric Field (Parallel Plates)
Sample Problem
A 12-V battery maintains the
electric potential difference
between two charged parallel
metal plates separated by 0.10m.
What is the electric field between
the plates?
Solution
V= 12 V
d = 0.10m
From V = Ed, we have E = V/d = 12 V/ 0.10m
= 1.2 x 102 V/m
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Relation between Electric Potential and
Electric Field (Parallel Plates)
Sample problem
Two parallel conducting plates are
charged to a voltage of 50V. If the
separation between the plates is 0.05m,
calculate the electric field between
them.
Solution
E= V/d = 50V/0.050m = 1000V/m
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Uses of parallel metal plate conductors
in everyday life
 Televisions, Oscilloscopes, Monitors, etc. use an electron beam steered
by electric fields to light up the (phosphorescent) screen at specified
points
screen
+ + + + + + +
cathode emitter
E-field
Why does the
beam ocurve
toward the
positive plate?
- - - - - - -
electron beam
metal plates
22
What the heck is going on?
Additional Resources
The Mechanical Universe
Video : Potential and
Capacitance
MIT University LECTURE#1
The Physics Classroom
Video Gravitational PE vs Electrical PE
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Summary
• The change in PE (Work) of a charge q when it moves
through a potential difference V is W =qV
•Potential difference is measured in volts (1V=1J/C) and is
sometimes referred to as voltage (V).
•The electric potential (V) at any point in space is defined as
the electric potential energy per unit charge
(joules/coulumbs).
•Electric potential difference (V) is equal to work done to
move charge from one point to another divided by the
charge. (V = W/q)
• The potential difference V between two points where a
uniform electric field E exists is given by V=Ed
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