lecture 4.2 : electric potential continued...4 a positive charge increases in potential energy as it...
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Lecture 4.2 :!Electric Potential Continued
Lecture Outline:!Electric Potential!
Potential Inside a Parallel-Plate Capacitor!Potential of Point Charges!
Feb. 5, 2015
Textbook Reading:!Ch. 28.4 - 28.7
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Announcements
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!
•HW4 due next Tue. (2/10) at 9am on Mastering Physics. !
•Exam #1 next Thu. (Feb. 12). Covers Ch. 25-28.
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Last Lecture...
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Define s=0 at negative plate, and U0 is potential at s=0.
We discussed the potential energy (U) associated with the location (s) of a charge (q) in an external electric field (E).
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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.
∆U=qE∆s
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Clicker Question #1
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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.
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Electric Potential Energy
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Example problem: Proton/Electron in a
2.0 cm x 2.0 cm parallel plate
capacitor
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Clicker Question #2
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A positive charge moves as shown. Its kinetic energy
A. Increases.
B. Remains constant.
C. Decreases.
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Potential Energy of Point Charges
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Potential energy shared by two point charges
Looks like Coulomb’s Law, but it’s different!
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Potential Energy of Point Charges
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Two like-sign point charges launched at each other:
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Potential Energy of Point Charges
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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?
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Clicker Question #3
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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.
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Potential Energy of a Dipole
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Electric Potential
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Alessandro Volta
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.
V � Uq+sources
q
1 volt = 1 V ≡ 1 J/C
Electric Potential:
1.5 V Battery
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Electric Potential
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�U = q�V
�V = Potential Difference, or Voltage.
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Electric Potential
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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 #4
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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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Potential Inside a Parallel Plate Capacitor
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Clicker Question #5
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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. v2 > v3. B. v2 = v3. C. v2 < v3. D. 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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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
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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
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3D Map of Potential around a positive charge.!How would the potential for a negative charge look?
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Clicker Question #6
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What is the ratio VB/VA of the electric potentials at the two points?!A. 9. B. 3. C. 1/3. D. 1/9. E. Undefined without knowing the charge.
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Potential of Point Charges
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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?
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Potential of Point Charges
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V =�
i
1
4⇥�0
qiri
3D Map of Potential around dipole.
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Potential of Point Charges
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What is the potential at the point indicated?
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Clicker Question #7
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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
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Continuous distributions of charge?
Vring on axis =1
4⇥�0
Q�R2 + z2
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Reminders
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!
•Stay up to date on your textbook reading. You should finish reading Ch. 28.!
•HW4 due on Tuesday (2/10).!•Exam #1 next Thursday. !