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Chapter 20
Electric Forces and Fields
Topics:
• Electric charge
• Forces between charged
•
•
objects
The field model and the
electric field
Forces and torques on
charged objects in electric
fields
Sample question:
In electrophoresis, what force causes DNA fragments to migrate
through the gel? How can an investigator adjust the migration rate?
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Slide 20-1
Conductors and Electric Fields
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Slide 20-55
Consider an infinite sheet of charge
h
Q
E=
where h =
2e 0
A
• Epsilon nought, e 0 = 8.85 ´ 10
-12
C2
N × m2
is electric permitivity of free space
• Electric permitivity is a measure of how well
electric field can pass through space or
materials
Discuss charge density
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Consider two infinite sheets of charge
What is the E-field at
points A, B, and C ?
Case 1:
A
B
C
Qleft = +Q
Qright = -Q
Case 2:
Qleft = 2Q
Qright = Q
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Checking Understanding
Two parallel plates have charges of equal magnitude but opposite
sign. What change could be made to increase the field strength
between the plates?
A.
B.
C.
D.
E.
Increase the magnitude of the charge on both plates
Decrease the magnitude of the charge on both plates
Increase the distance between the plates
Decrease the distance between the plates
Increase the area of the plates (while keeping the magnitude of
the charges the same)
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Answer
Two parallel plates have charges of equal magnitude but opposite
sign. What change could be made to increase the field strength
between the plates?
A.
B.
C.
D.
E.
Increase the magnitude of the charge on both plates
Decrease the magnitude of the charge on both plates
Increase the distance between the plates
Decrease the distance between the plates
Increase the area of the plates (while keeping the magnitude of
the charges the same)
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Chapter 21 Key Equations (Physics 151)
Key Ideas on Energy from Physics 151
Dot Product
Energy Bar Charts
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Slide 21-16
Chapter 21 Key Equations (Physics 151)
Key Energy Equations from Physics 151
Definition of Work
Work W = F i Dr = F Dr cos a
Work- Energy Theorem (only valid when particle model applies)
Wnet = DKE
Work done by a conservative force (Fg, Fs, & Fe)
Wg = -DPEg Also work done by conservative force
is path independent
Conservation of Energy Equation
KEi +
å
PEi + D Esys = KE f +
different types
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å
PE f + DEth
different types
Slide 21-16
Review of Work
Definition of Work: Work W = F i Dr = F Dr cos a
where a = 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
Electric Potential Energy
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Slide 21-9
Chapter 21 Key Equations (2)
Key Energy Equations from Physics 152
q1q2
PEe = k
r12
Electric Potential Energy for 2 point charges
(zero potential energy when charges an infinite distance apart)
Potential Energy for a uniform infinite plate
DPEe = -We = - éë Fe × Dr cos a ùû = - ( q E ) Dr cos a
For one plate, zero potential energy is at infinity
For two plates, zero potential energy is at one plate or
inbetween the two plates
Electric Potential V and Change in Electric Potential => ΔV
PEe
V=
qtest
DPEe
We
DV =
=qtest
qtest
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Slide 21-16
Example: Electric Potential Energy
A cart on a track has a large, positive charge and is located between
two sheets of charge. Initially at rest at point A, the cart moves
from A to C.
a. Draw qualitative force diagrams for
the cart at positions A, B and C.
b. Draw qualitative energy bar charts
for the cart when it is at each position
A, B and C. List the objects that
make up your system:
c. How would your force and energy diagrams change (if at all) if the sheet to
the right were also positively charged?
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Slide 21-16
Changes in Electric Potential Energy ΔPEe
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)
Greatest ΔPEe
(a)
(b)
(c)
(d)
Hydrogen Atom
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Slide 21-16
Changes in Electric Potential Energy ΔPEe
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)
Greatest ΔPEe
(e)
(f)
(g)
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Slide 21-16
Changes in Electric Potential Energy ΔPEe
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
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 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 ΔV= 0 V is an equipotential line
(The electric force does zero work on a test charge that moves
on an equipotential line and ΔPEe= 0 J)
For a point charge
q
1 q
V=K =
r 4pe 0 r
For very large charged plates, must use
DPEe
We
Fe i Dr
qtest E i Dr
DV =
==== -E i Dr = - E Dr cos a
qtest
qtest
qtest
qtest
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Slide 21-16
Electric Potential and E-Field for Three Important Cases
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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
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