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Chapter 21
Electric Potential
Topics:
•
Electric energy
(Electric Potential Energy)
• Electric potential
• Gravitation Energy &
Potential
•
Conservation of energy
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?
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Chapter 21 Key Ideas (Physics 151)
Dot Product
Method for multiplying two vectors to get a scalar
Definition of Work
consta
nt
Work is how forces add energy to or take away energy from a
system. It is the effect of a force applied over a displacement.
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Chapter 21 Key Equations (Physics 151)
Key Energy Equations from Physics 151
Types of Energy
Conservation of Energy Equation (key concept)
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Slide 21-16
Energy Bar Graph
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Chapter 21 Key Equations (2)
Key Energy Equations from Physics 152
Work done by a conservative force (Fg, Fs, & Fe)
Also work done by conservative force
Wg = -DPEg is path independent
q1q2
PEe = k
r12
Electric Potential Energy for 2 point charges
(zero potential energy when charges an infinite distance apart)
elta Potential Energy for a uniform infinite plate
For one plate, zero potential energy is at infinity
For two plates, zero potential energy is at one plate or
inbetween the two plates
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Changes in Electric Potential Energy elta PEe
For each situation below, identify which arrangement (final or initial) has more
electrical potential energy within the system of charges and their field.
Initial (A)
Final (B)
(a)
(b)
(c)
(d)
Hydrogen Atom
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Greatest Delta
PEe
Changes in Electric Potential Energy elta PEe
For each situation below, identify which arrangement (final or initial) has more
electrical potential energy within the system of charges and their field.
Initial (A)
Final (B)
(e)
(f)
(g)
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Greatest elta
PEe
Changes in Electric Potential Energy elta 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 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
Gravitational Potential Energy: Example Problem 2
A spacecraft is launched away from earth
a. Draw several gravitational field lines
in the region around Earth.
b. Determine the change in
gravitational potential energy when
the spacecraft moves from A to B,
where A is 10 million miles from
Earth and B is 30 million miles from
Earth.
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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
Electric Potential Model Worksheet 2:
Energy and Potential in Uniform Fields
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
Uelec = qV; V = U elec / q
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Slide 21-10
Chapter 21 Key Equations (3)
Key Points about Electric Potential
Electric Potential is the Electric Potential Energy per Charge
PEe
V=
qtest
DPEe
We
DV =
=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 V= 0 V is an equipotential line
(The electric force does zero work on a test charge that moves
on an equipotential line and 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 4pe 0 r
For very large charged plates, must use
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Slide 21-25
Checking Understanding
Rank in order, from largest to smallest, the electric
potentials at the numbered points.
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Slide 21-14
Example Problem
A proton has a speed of 3.5 x 105 m/s at a point where the
electrical potential is 600 V. It moves through a point where the
electric potential is 1000 V. What is its speed at this second point?
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Slide 21-16
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Slide 21-15
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 V
• Higher potential as you approach a positive charge; lower potential as you
approach a negative charge
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Slide 21-16
A Topographic Map
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
Equipotential Maps (Contour Maps)
1.Describe the charges that could
create equipotential lines such as
those shown above.
2.
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