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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

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.

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

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.

Electric Potential Energy

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Example problem: Proton/Electron in a

2.0 cm x 2.0 cm parallel plate

capacitor

Clicker Question #2

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A positive charge moves as shown. Its kinetic energy

A.  Increases.

B.  Remains constant.

C.  Decreases.

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!

Potential Energy of Point Charges

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Two like-sign point charges launched at each other:

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?

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.

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

Electric Potential

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�U = q�V

�V = Potential Difference, or Voltage.

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?

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.!

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!

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?

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.

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?

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.

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?

Potential of Point Charges

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V =�

i

1

4⇥�0

qiri

3D Map of Potential around dipole.

Potential of Point Charges

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What is the potential at the point indicated?

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.

Potential of Point Charges

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Continuous distributions of charge?

Vring on axis =1

4⇥�0

Q�R2 + z2

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. !