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PHYS 1110
Lecture 5
Professor Stephen Thornton
September 13, 2012
Reading Quiz
metal
conductor
(rod and sphere are not
touching)
A metal conductor has been
sitting for a very long time. We bring up a negatively
charged rod, close to, but not touching the conductor.
Which of the following is most true about this diagram?
A) The diagram is wrong, because charge is not
conserved.
B) The diagram looks okay.
C) The diagram is wrong, because the charge
configuration is unlikely.
Answer: C
A is not correct, because charges do not
have to be conserved. There was charge
on the Teflon rod.
C is correct, because the negative charge
on the conductor would be repelled by
the negative charge on the rod and move
away.
Rub a Teflon
rod on fur.
See what
happens. Try to
pick up pieces of
paper.
When we rub one
item on another,
electrons are
rubbed off one item
to the other.
Discuss atomic
model.
Rabbit fur
++++++
Glass
+++++
Human hair
++++
Nylon
+++
Silk
++
Paper
+
Cotton
-
Wood
--
Amber
---
Rubber
----
PVC
-----
Teflon
------
Electrical Polarization
Polar
molecules
(water H2O,
ammonia NH3,
hydrogen
fluoride HF)
Look at demo:
2 x 4 on watch glass.
How does Teflon rod cause board to
move?
Benjamin Franklin is the one who named the
charges positive and negative. We now know
the electrons (which are mobile and carry
charge) are negative.
Law of conservation of charge: the net
amount of charge is conserved in any process.
We are dealing with Electrostatics- charges at
rest.
Conductors are materials that conduct
charge easily. Examples are metals like
aluminum, copper, iron, etc.
Insulators are materials that do not
conduct charge easily. Examples are
glass, plastics, ceramics (nonmetallic).
Semiconductors are materials that are
between conductors and insulators and
can conduct charge under special
conditions like at high temperatures.
What about water and air?
Water is a polar molecule.
Air is mostly N 2 , O 2 , not
easily polarized.
Look at this You Tube video for
the dangers of electrostatics.
Let’s consider some experiments
and see what happens.
1) Like charges repel and unlike charges attract.
2) If we vary the distance between point charges, we find
the force becomes smaller as the separation distance
1
increases.
F
r2
3) If we vary the charge magnitude, we find F ~ q1q2
4) Put these results together and obtain the Coulomb force.
kq1q2
1
F  2 where k 
 8.99  10
r
4 0
9
Nm / C
2
2
Forces Between Point Charges
kq1q2
F12  2 êr
r
F12 is force on 1 due to 2.
Superposition of Forces
qq
F  1 2 êr
12 4 r 2
0
We find the total force by
adding the vector sum of
the individual forces.
Conceptual Quiz
A
Conceptual Quiz
B
C
Which of the arrows best
D
represents the direction
of the net force on charge
d
+2Q
+Q
+Q due to the other two
charges?
d
+4Q
E
A
Conceptual Quiz
B
C
Which of the arrows best
D
represents the direction
of the net force on charge
d
+2Q
+Q
+Q due to the other two
d
charges?
+4Q
The charge +2Q repels +Q toward the
right. The charge +4Q repels +Q
upward, but with a stronger force.
Therefore, the net force is up and to
+2Q
the right, but mostly up.
Follow-up: What would happen if
the yellow charge were +3Q?
+4Q
E
Electric field
What is a field? Why do we want to learn
about them?
Discuss fields in general
temperature (use thermometer)
gravitation (use test mass)
pressure (weather maps)
An Electrostatic Force Field
Use a small test
charge q0 to
find force due
to charge +q.
q0
Definition of Electric Field
qq
F  k 20
r
F is force between charge q
and test charge q0 (small).
The test charge is used to map out the electric
field due to charge q.
F kq
E  = 2 eˆ r Electric field due to a charge
q0 r
q (not q0 ). Unit: N/C
Electric Field of a Point Charge
F kq
E  = 2 eˆ r
q0 r
E  k q2
r
k 1
4 0
The Direction of the
Electric Field for
Point Charges
Superposition of the Electric Field
q2
E2  k 2
d
q1
E1  k 2
d
Imagine the test charge could be
placed here. The test charge is
only useful to imagine the force
field.
Relation between F and E
If we put a charge q1 in an electric field E ,
then the charge q1 feels a force of value
F1  q1E
This is the really useful part.
Don’t confuse this charge q1 with the
test charge q0 or the original charges q
that produced E. The test charge q0
was used to find the electric field. This
is a real charge q1 placed in the electric
field.
Determining electric fields
Rules and hints:
1) E lines start on + charges, end on – charges.
Can start and stop at infinity.
2) Place test charge q0 at any point and find
direction of force on q0 to determine E line.
3) E lines can never intersect!
4) E lines are more dense when magnitude is
greater.
Electric Field Lines for a Point Charge
Electric Field Lines for
Systems of Charges
We call this
a dipole. It
is a dipole
field.
Conceptual Quiz
Which of the charges
has the greater
magnitude?
A)
B)
C) both the same
Conceptual Quiz
Which of the charges
has the greater
magnitude?
The field lines are denser around
the red charge, so the red one
has the greater magnitude.
Follow-up: What is the red/green ratio
of magnitudes for the two charges?
A)
B)
C) both the same
The Electric Field of a
Charged Plate

E
2 0
s is charge per unit area of plate
Parallel charged plates
Correct
Charge Distribution
on a Conducting Sphere
If charges were inside the
sphere, they would repel
each other. Also E must be
zero inside conductor or
free electrons would move.
Wrong
Charges placed on a
metal conductor must
reside on the surface.
The electric field near a conducting
surface must be perpendicular to the
surface when in equilibrium.
If we place conductor in electric field,
the E lines must be  to surface. If not,
charges would move. E must be zero inside.
F  q0 E
W  F s work
U  W   qE s
Ignore gravity
Where does this
electric field come
from?
The charge q0 feels a force due to E.
The electric field E does work on the charge.
The charge has a higher potential energy on the left
than it does on the right.
The charge gains kinetic energy in the electric field.
Change in Electric Potential Energy
Who (or what) is doing work here?
Change in Electric Potential Energy
Electric field
Gravitational field
Who (or what) is doing work here?
Electric Potential V
U W
V 

q0
q0
Unit: J/C = volt, V
definition!!
Electric potential, or potential, is one of
the most useful concepts in
electromagnetism. This is a biggie!!
(notice that it has its own unit!)
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:
U b - U a = - W = - qEd
The electric field does work to move
the positive charge q from a to b.
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Electric potential can be thought of as
potential energy per unit charge:
Ua
Va =
q
DU
DV =
q
It is really only the change in electric potential
that is important, and we define it that way.
Only changes in electric potential (or simply
called potential) can be measured, allowing
free assignment of V = 0. For example, we
can let one of the voltages be zero at infinity.
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Electrical sources
such as batteries and
generators supply a
constant potential
difference. Here are
some typical potential
differences, both
natural and
manufactured:
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Energy conservation
Energy conservation relations are still valid.
K A  U A  KB  U B
If we look at definition of V ,
U
we have V 
, so U  qV
q
K B  K A  U A  U B  q (VA  VB )
The change in kinetic energy is proportional
to the change in electric potential!!
Notes on electric potential
kq
Point charge V 
r
Scalar quantity, not vector like electric field.
For multiple charges, we simply add the
potentials from each charge for simple
superposition!
In practice, we use potential concept much
more than electric field. We can measure
potential easily, but not electric field.
Electric Potential Energy
Electric potential energy for two point charges,
q and q0, separated by a distance r, is simply
q0 q
U  q0V  k
r

Conceptual Quiz. A proton is released from the +
plate as shown, and an electron is released from the –
plate. Which particle has the greatest kinetic energy
when it reaches the other plate?
A) proton
B) electron
C) the kinetic energies are the same.
Answer: C
The particles experience the same
electric field and have the same
charge. The kinetic energy increase
is equal to the work done by the
electric field. W = Fd = qEd

Conceptual Quiz. A proton is released from the +
plate as shown, and an electron is released from the –
plate. Which particle has the greatest speed when it
reaches the other plate?
A) proton
B) electron
C) the speeds are the same.
Answer: B
We just saw that the proton and electron
will have the same kinetic energy
increase. But K = mv2/2, and because
the electron has such a smaller mass, its
velocity must be much greater than that
of the proton.
Conceptual Quiz
A
At which point
E) all of them
does V = 0?
B
+Q
C
D
kq
V
r
–Q
Conceptual Quiz
A
E) all of them
At which point
does V = 0?
B
+Q
C
–Q
D
All of the points are equidistant from both charges. Since
the charges are equal and opposite, their contributions to
the potential cancel out everywhere along the mid-plane
between the charges.
Follow-up: What is the direction of the electric field at all 4 points?
Equipotential Surfaces
kq
V=
r
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.
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Equipotential Surfaces
The electric field does no work by
moving a charge perpendicular to
the electric field, which is along
the equipotential!
Another case showing electric
field lines are perpendicular to
equipotentials.
The surface of a conductor is an
equipotential.
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Electrostatic precipitators- demo
Capacitance
Simplest capacitor – two equal
and oppositely charged
conductors
Parallel-plate
capacitor:
A capacitor consists of two
conductors that are close but
not touching. A capacitor has
the ability to store electric
charge.
When a capacitor is connected to a battery, the
charge on its plates is proportional to the
voltage:
Q = CV
The quantity C is a constant called capacitance.
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Capacitance
If Q = CV,
Q
C
V
C
1F = 1
V
C
Unit:
= farad or F
V
Parallel plate capacitor
Q d

V  Ed  d 
A 0
0
Q 0 A
So
V

d
and
Q 0 A
C 
d
V
The capacitance
value depends only
on geometry!
Dielectric
Effect of a Dielectric on the
Electric Field of a Capacitor
E  E0
E  E0 /  and V  V0 /
where  is the dielectric
constant
The induced electric field
reduces the overall field:
• Dielectric = insulator
• Molecules act as dipoles,
permanent or induced
• This effectively reduces the
electric field
A dielectric is an insulator, and is
characterized by a dielectric constant k .
Capacitance of a parallel-plate capacitor filled
with dielectric:
C  0 A
d
C  C0
for parallel-plate capacitor
Using the dielectric constant, we define the
permittivity:
   0
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Dielectrics
Dielectric strength is the
maximum electric field a
dielectric can experience
without breaking down.
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Energy Required to
Charge a Capacitor
Move charge D Q across
plates. It takes work
W and increases U.
U  W  V Q
Sum over the Q
2
Q
1
1
2
U
 QV  CV
2C 2
2
Capacitor energy storage
Electric Energy Storage
Energy stored in a capacitor.
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