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Transcript
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
1
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%
2
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.
3
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.
4
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!
5
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
6
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
7
Electric Potential
What is the speed of a proton that has been accelerated
from rest through a potential difference of -1000V?
8
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.
9
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!
10
Potential Inside a Parallel Plate Capacitor
11
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?
12
Potential Inside a Parallel Plate Capacitor
Batteries are sources of potential differences!
Think of water being pumped up a
hill, then flowing back downhill.
13
Potential of Point Charges
3D Map of Potential around a positive charge.
14
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.
15
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?
16
Potential of Point Charges
V =
�
i
1 qi
4π�0 ri
3D Map of Potential around dipole.
17
Potential of Point Charges
What is the potential at the point indicated?
18
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.
19
Potential of Point Charges
Continuous distributions of charge?
Vring
20
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.
21