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Chapter 21
Electric Potential
Topics:
• 
• 
• 
• 
Conservation of energy
Work and Delta PE
Electric potential energy
Electric potential
Sample question:
Shown is the electric potential measured on the surface of a patient.
This potential is caused by electrical signals originating in the beating
heart. Why does the potential have this pattern, and what do these
measurements tell us about the heart s condition?
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Slide 21-1
Most Pressing Questions
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Chapter 21 Key Energy Equations
Key Energy Equations from Physics 151
!
! ! !
Definition of Work Work!!W = F!i!!r = F !r cos "
Where ! = angle between the vectors
Work done by a conservative force (Fg, Fs, & Fe) We = !"PEe
Also work done by conservative force is path independent
Conservation of Energy Equation
(can ignore PEg and PEs unless they are relevant)
KEi +
!
PEi + " Esys = KE f +
different !types
!
PE f + "Eth
different !types
Electric Energy – Special Cases (Similar equations for gravity)
qq
2 Point Charges PE = k 1 2
e
r12
Charge in a
Uniform E-field
!
!
!
!PEe = "We = " %& Fe # !r cos $ '( = " q E !r cos $
Note: in both cases of Electric Energy must assume where PEe = 0
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Slide 21-16
Review of Work
!
! ! !
Definition of Work: Work!!W = F!i!!r = F !r cos "
where ! = angle between the vectors
•  Calculate the work done in moving each ball from y = 0 meters to y = 5 meters
•  Calculate the work per kg for moving each ball from y = 0 m to 5 m
•  Calculate the change in gravitational potential energy per kg for moving each
ball from = 0 m to 5 m
•  Calculate the speed each ball would have as it reached the ground if released
from 5 meters above the ground
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Slide 21-16
Changes in Electric Potential Energy – Delta PEe
Is the change ∆PEe of a + charged particle positive, negative,
or zero as it moves from i to f?
(a) Positive (b) Negative (c) Zero (d) Can t tell
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Slide 21-11
Electric Potential Model Worksheet Problems: "
Rank the change in gravitational potential energy for the following lettered objects in the
Earth s gravitational field.
a. . most  _______ _________ ________ ________ _______ _______ ________
b. Explain your ranking, stating why each is greater than, less than, or equal to its
neighbors.
c. Where is the energy stored? What gains or loses energy as the masses move from one
place to another?
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Slide 21-16
Electric Potential Energy Example Problem
The electric field between two
charged plates is uniform with a
strength of 4 N/C.
a. Draw several electric field lines in the
region between the plates.
b. Determine the change in electrical
potential energy in moving a positive
4 microCoulomb charge from A to B.
c. Determine the change in electrical potential energy in moving a
negative 12 microCoulomb charge from A to B.
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Slide 21-16
Electric Potential Energy: Example Problem 3
A small charge moves farther from a
positive source charge.
a. Draw several electric field lines in the region
around the source charge.
b. Determine the change in electrical potential
energy in moving a positive 4 nC charge
from A to B, where A is 3 cm from the source
charge and B is 10 cm away.
c. Determine the change in electrical potential
energy in moving a negative 4 nC charge
from A to B.
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Slide 21-16
The V field
• Can we describe electric fields using the
concepts of work and energy? • To do so, we need to describe the electric
field not as a force-related E field, but as an
energy-related field.
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Electric Potential
U elec = qV; V = U elec / q
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<= Replace
before using
Slide 21-10
Chapter 21 Key Equations (3)
Key Points about Electric Potential
Electric Potential is the Electric Potential Energy per Charge
V=
PEe
!!
qtest
!V =
!PEe
W
=" e
qtest
qtest
Electric Potential increases as you approach positive source
charges and decreases as you approach negative source
charges (source charges are the charges generating the electric
field)
A line where Delta V= 0 V is an equipotential line
(The electric force does zero work on a test charge that moves
on an equipotential line and Delta PEe= 0 J)
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Slide 21-16
Electric Potential and E-Field for Three Important Cases
For a point charge
q
1 q
V=K =
r 4!" 0 r
For very large charged plates, must use
!
!
!
!
!
! !
!PEe
We
Fe !i!!r
qtest E!i!!r
!
!V =
="
="
="
= " E!i!!r = " E !r cos #
qtest
qtest
qtest
qtest
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Slide 21-25
Finding the electric potential energy when the V field is known
•  If we know the electric potential at a specific
location, we can rearrange the definition of the V
field to determine the electric potential energy:
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The superposition principle and the V field
due to multiple charges
• where Q , Q , Q , … are the source charges
1
2
3
(including their signs) creating the field and r1, r2, r3,
… are the distances between the source charges
and the location where we are determining the V
field.
• So Electric Potentials (V) add just like Electric Potential Energies
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Checking Understanding
Rank in order, from largest to smallest, the electric
potentials at the numbered points.
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Slide 21-14
Quantitative Example
•  Suppose that the heart's dipole charges −Q and +Q are separated
by distance d. Write an expression for the V field due to both
charges at point A, a distance d to the right of the +Q charge.
1.  Simplify and diagram.
2.  Represent mathematically.
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Example Problem
For the situation shown in the figure, find
A.  The potential at points a and b.The potential difference between
a and b.
B.  The potential energy of a proton at a and b.
C.  The speed at point b of a proton that was moving to the right at
point a with a speed of 4.0 x 105 m/s.
D.  The speed at point a of a proton that was moving to the left at
point b with a speed of 4.0 x 105 m/s.
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Slide 21-22
Particles in a potential difference
• A positively charged object accelerates from
regions of higher electric potential toward
regions of lower potential (like an object
falling to lower elevation in Earth's
gravitational field).
• A negatively charged particle tends to do the
opposite, accelerating from regions of lower
potential toward regions of higher potential. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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Slide 21-15
A Topographic Map
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Slide 21-12
Topographic Maps
1. Describe the region
represented by this map.
2. Describe the directions a
ball would roll if placed at
positions A – D.
3. If a ball were placed
at location D and
another ball were placed
at location C and both were
released,
which would have the greater acceleration?
Which has the greater potential energy when released?
Which will have a greater speed when at the bottom of the hill?
4. What factors does the speed at the bottom of the hill depend on? What factors
does the acceleration of the ball depend on?
5. Is it possible to have a zero acceleration, but a non-zero height? Is it possible
to have a zero height, but a non-zero acceleration?
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Slide 21-16
E-field lines and Equipotential lines
E-field Lines
•  Go from + charges to - charges
•  Perpendicular at surface of conductor or charged surface
•  E-field in stronger where E-field lines are closer together
•  More charge means more lines
Equipotential Lines
•  Parallel to conducting surface
•  Perpendicular to E-field lines
•  Near a charged object, that charges influence is greater, then blends as
you to from one to the other
•  E-field is stronger where Equipotential lines are closer together
•  Spacing represents intervals of constant Delta V
•  Higher potential as you approach a positive charge; lower potential as you
approach a negative charge
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Slide 21-16
Equipotential Maps (Contour Maps)
1. Describe the charges that
could create equipotential lines
such as those shown above.
2. Describe the forces a proton
would feel at locations A and B.
3.  Describe the forces an
electron would feel at locations
A and B 4. Where could an electron be
placed so that it would not
move?
5. At
which point is the magnitude of the electric field the greatest?
6. Is it possible to have a zero electric field, but a non-zero electric potential?
7. Is it possible to have a zero electric potential, but a non-zero electric field?
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Slide 21-16
3D view
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Slide 21-16
Graphical Representations of Electric Potential
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Slide 21-13
Example Problem
Source charges create the electric potential shown below.
A.  Rank the Electric Fields at
points A, B, C, and D
B.  Rank the Electric Potentials
at points A, B, C, and D
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Slide 21-33
Example Problem
Source charges create the electric
potential shown.
A.  What is the potential at point
A? At which point, A, B, or C,
does the electric field have its
largest magnitude?
B.  Is the magnitude of the electric
field at A greater than, equal
to, or less than at point D?
C.  What is the approximate magnitude of the electric field at
point C?
D.  What is the approximate direction of the electric field at
point C?
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Slide 21-33
Example Problem
A proton is released from rest at point a. It then travels past point
b. What is its speed at point b?
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Slide 21-23
Applications of Electric Forces and Fields
•  In electrophoresis, what force causes DNA
fragments to migrate through the gel? How
can an investigator adjust the migration rate?
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Electric Force & Field Applications
•  To get the colored lines
produced by gel
electrophoresis of a sample of
DNA, you put the sample of
DNA into a solution, then cut
the DNA into fragments by
enzymes.
•  In the solution, the fragments
have a negative charge.
•  Drops of the solution (with DNA fragments) are
placed in wells at one end of a container of gel.
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Electric Force & Field Applications
•  Electrodes at opposite
ends of the container of
gel produce an electric
field that exerts an
electric force on the
DNA fragments.
•  Drag forces cause some
fragments of different
sizes to migrate at
different rates. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Electric Force & Field Applications
•  After time, the fragments sort
into distinct lines, creating a
“genetic fingerprint.”
•  Two identical DNA samples
would produce the same
fragments and therefore the
same pattern.
•  It is extremely unlikely that
two unrelated DNA samples
would produce the same
pattern.
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Electric Dipoles
• An electric dipole is two equal but
opposite charges with a separation between
them. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Electric Dipoles
•  When the polarization is caused by an external charge, the atom
has become an induced electric dipole. •  Because the negative end of the dipole is slightly closer to the
positive charge in this figure, the attractive force on the negative
end exceeds the repulsive force on the positive end. •  There is a net force toward the external charge.
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Hydrogen Bonding
• Some molecules have an asymmetry in their charge distribution that makes them permanent electric
dipoles.
• In a water molecule, bonding between the hydrogen and oxygen atoms results in an unequal
sharing of charge that leaves the hydrogen atoms
with a small positive charge and the oxygen atom
with a negative charge. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Hydrogen Bonding
• A hydrogen bond is the weak bond between the hydrogen atom of one molecule of water and the negative oxygen atom in the second molecule.
• These weak bonds give water its “stickiness” responsible for properties such as expansion on freezing.
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Hydrogen Bonding
•  Hydrogen bonds are extremely important in biological
systems.
•  The nucleotides, the four molecules guanine, thymine,
adenine, and cytosine, on one strand of a DNA helix
form hydrogen bonds with the nucleotides on the
opposite strand.
•  The nucleotides bond only in certain pairs. This
preferential bonding is due to hydrogen bonds. The
positive hydrogen atoms on one nucleotide attract the
negative oxygen or nitrogen atoms on another. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Hydrogen Bonding
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The Electric Field of the Heart
•  The surface of the heart is
positive on one side of the
boundary between tissue
that is polarized and tissue
that is not yet depolarized,
negative on the other.
•  The heart is a large electric
dipole. The orientation and
strength of the dipole
change during each beat of
the heart.
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