Lecture 4.2 :!
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. 5, 2015
1
Announcements
!
•HW4 due next Tue. (2/10) at 9am on Mastering Physics.
•Exam #1 next Thu. (Feb. 12).
Covers Ch. 25-28.
2
!
Last Lecture...
We discussed the potential energy (U) associated with the
location (s) of a charge (q) in an external electric field (E).
Define s=0 at negative plate, and U0 is potential at s=0.
3
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.
∆U=qE∆s
Analogous to lifting an object above the earth to
increase its potential energy.
4
Clicker Question #1
Two positive charges are
equal. Which has more
electric potential energy?
A.  Charge A.
B.  Charge B.
C.  They have the same potential energy.
D.  Both have zero potential energy.
5
Electric Potential Energy
Example problem:
Proton/Electron in a
2.0 cm x 2.0 cm
parallel plate
capacitor
6
Clicker Question #2
A positive charge moves
as shown. Its kinetic
energy
A.  Increases.
B.  Remains constant.
C.  Decreases.
7
Potential Energy of Point Charges
8
Potential energy shared by two point charges
Looks like Coulomb’s Law, but it’s different!
9
Potential Energy of Point Charges
Two like-sign point charges launched at each other:
10
Potential Energy of Point Charges
Two opposite-sign point charges launched away
from each other:
Emech<0 implies a bound system. Can you think of any other
bound systems in nature?
11
Clicker Question #3
A positive and a negative charge are
released from rest in vacuum. They
move toward each other. As they do:
A.  A positive potential energy becomes more positive.
B.  A positive potential energy becomes less positive.
C.  A negative potential energy becomes more negative.
D.  A negative potential energy becomes less negative.
E.  A positive potential energy becomes a negative
potential energy.
12
Potential Energy of a Dipole
13
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:
V
Uq+sources
q
1 volt = 1 V ≡ 1 J/C
Alessandro Volta
1.5 V Battery
14
Electric Potential
V = Potential Difference, or Voltage.
U =q V
15
Electric Potential
What is the speed of a proton that has been accelerated
from rest through a potential difference of -1000V?
16
Clicker Question #4
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.!
17
Potential Inside a Parallel Plate Capacitor
18
Clicker Question #5
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!
19
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?
20
Potential Inside a Parallel Plate Capacitor
Batteries are sources of potential differences!
Think of water being pumped up a
hill, then flowing back downhill.
21
Potential of Point Charges
3D Map of Potential around a positive charge.!
How would the potential for a negative charge look?
22
Clicker Question #6
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.
23
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? What potential energy does the electron have?
24
Potential of Point Charges
V =
i
1 qi
4⇥ 0 ri
3D Map of Potential around dipole.
25
Potential of Point Charges
What is the potential at the point indicated?
26
Clicker Question #7
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.
27
Potential of Point Charges
Continuous distributions of charge?
Vring
28
on axis
1
=
4⇥ 0
Q
R2 + z 2
Reminders
!
•Stay up to date on your textbook reading.
should finish reading Ch. 28.!
•HW4 due on Tuesday (2/10).!
•Exam #1 next Thursday. !
29
You