lecture 4.2 : electric potential continued...4 a positive charge increases in potential energy as it...

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1 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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Page 1: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

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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

Page 2: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

Announcements

2

!

•HW4 due next Tue. (2/10) at 9am on Mastering Physics. !

•Exam #1 next Thu. (Feb. 12). Covers Ch. 25-28.

Page 3: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

Last Lecture...

3

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).

Page 4: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

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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

Page 5: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

Clicker Question #1

5

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.

Page 6: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

Electric Potential Energy

6

Example problem: Proton/Electron in a

2.0 cm x 2.0 cm parallel plate

capacitor

Page 7: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

Clicker Question #2

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A positive charge moves as shown. Its kinetic energy

A.  Increases.

B.  Remains constant.

C.  Decreases.

Page 8: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

Potential Energy of Point Charges

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Page 9: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

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Potential energy shared by two point charges

Looks like Coulomb’s Law, but it’s different!

Page 10: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

Potential Energy of Point Charges

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Two like-sign point charges launched at each other:

Page 11: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

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?

Page 12: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

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.

Page 13: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

Potential Energy of a Dipole

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Page 14: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

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

Page 15: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

Electric Potential

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�U = q�V

�V = Potential Difference, or Voltage.

Page 16: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

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?

Page 17: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

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.!

Page 18: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

Potential Inside a Parallel Plate Capacitor

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Page 19: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

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!

Page 20: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

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?

Page 21: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

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.

Page 22: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

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?

Page 23: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

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.

Page 24: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

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?

Page 25: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

Potential of Point Charges

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V =�

i

1

4⇥�0

qiri

3D Map of Potential around dipole.

Page 26: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

Potential of Point Charges

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What is the potential at the point indicated?

Page 27: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

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.

Page 28: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

Potential of Point Charges

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Continuous distributions of charge?

Vring on axis =1

4⇥�0

Q�R2 + z2

Page 29: Lecture 4.2 : Electric Potential Continued...4 A Positive charge increases in potential energy as it approaches the positive side of a capacitor. Since energy is conserved, its kinetic

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. !