Lecture 5.1 :
Electric Potential Continued
Lecture Outline:
Electric Potential
Potential Inside a Parallel-Plate Capacitor
Potential of Point Charges
Textbook Reading:
Ch. 28.4 - 28.7
Feb. 11, 2013
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Announcements
•HW5 due next Mon. (2/18) at 9pm on Mastering Physics.
•Please fill out the clicker form I e-mailed if you haven’t already.
•Due to special colloquium today, my office hours today will be cut
short ( 3:00-3:45pm). Let me know if you would like to meet some
other time.
•Exam #1:
‣Average was 55.4% ± 15.0%
‣Curve: Your Curved Score = (Your UnCurved Score)^0.65 * 100^0.35
‣Example: You scored 50%.
Curved score = 50^0.65 * 100^0.35 = 63.7%
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Last Lecture...
We discussed the potential energy (U) associated with the
location of a charge (q) in an external electric field (E).
Define s=0 at negative plate, and U0 is potential at s=0.
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Last Lecture...
A Positive charge increases in potential energy as it
approaches the positive side of a capacitor. Since energy is
conserved, its kinetic energy must simultaneously decrease.
Analogous to lifting an object above the earth to
increase its potential energy.
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Last Lecture...
We derived the potential energy shared by two point
charges by calculating the Work done by one charge on the
other.
Looks like Coulomb’s Law, but it’s different!
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Electric Potential
We introducted “Electric Field” to indicate an
electric charge’s alteration of space. Now we
need a concept of potential energy at all points
in space due to a source charge.
Electric Potential:
Uq+sources
V ≡
q
1 volt = 1 V ≡ 1 J/C
Alessandro Volta
1.5 V Battery
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Electric Potential
Since Energy is always conserved, a charged object that is gaining
Potential Energy must lose the same amount of Kinetic Energy.
∆V = Potential Difference, or Voltage.
∆U = q∆V
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Electric Potential
What is the speed of a proton that has been accelerated
from rest through a potential difference of -1000V?
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Clicker Question #1
If a positive charge is released from rest, it
moves in the direction of
A. Higher electric potential.
B. Lower electric potential.
C. Need more information.
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Clicker Question #2
Two protons, one after the other, are
launched from point 1 with the same
speed. They follow the two trajectories
shown. The protons’ speeds at points 2
and 3 are related by
A.
B.
C.
D.
v2 > v3.
v2 = v3.
v2 < v3.
Not enough information to compare their speeds.
NOTE: This answer can be seen most easily if you use Energy
Conservation arguments. If you use kinematic arguments, be
careful to note that the two trajectories don’t take equal time!
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Potential Inside a Parallel Plate Capacitor
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Potential Inside a Parallel Plate Capacitor
Equipotential Surfaces are
surfaces with the same
value of V at every point.
Where are the
equipotentials in this
drawing?
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Potential Inside a Parallel Plate Capacitor
Batteries are sources of potential differences!
Think of water being pumped up a
hill, then flowing back downhill.
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Potential of Point Charges
3D Map of Potential around a positive charge.
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Clicker #3
What is the ratio VB/VA
of the electric potentials
at the two points?
A.
B.
C.
D.
E.
9.
3.
1/3.
1/9.
Undefined without knowing the charge.
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Potential of Point Charges
In a semiclassical model of the hydrogen atom, the
electron orbits the proton at a distance of 0.053nm.
What is the electric potential of the proton at the
position of the electron?
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Potential of Point Charges
V =
�
i
1 qi
4π�0 ri
3D Map of Potential around dipole.
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Potential of Point Charges
What is the potential at the point indicated?
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Clicker #4
At the midpoint between
these two equal but opposite
charges:
A. E = 0; V = 0.
B. E = 0; V > 0.
C. E = 0; V < 0.
D. E points right; V = 0.
E. E points left; V = 0.
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Potential of Point Charges
Continuous distributions of charge?
Vring
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on axis
1
Q
√
=
4π�0 R2 + z 2
Reminders
•Stay up to date on your textbook reading.
You
should finish reading Ch. 28, and start on Ch. 29.
•Begin working on HW5.
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