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Lecture 5.1 :Electric Potential Continued

Lecture Outline:Electric Potential

Potential Inside a Parallel-Plate CapacitorPotential of Point Charges

Feb. 11, 2013

Textbook Reading:Ch. 28.4 - 28.7

Announcements

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•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%

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 of a charge (q) in an external electric field (E).

Last Lecture...

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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.

Last Lecture...

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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!

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.

Since Energy is always conserved, a charged object that is gaining Potential Energy must lose the same amount of Kinetic Energy.

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 #1

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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.

Clicker Question #2

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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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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.

Clicker #3

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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?

Potential of Point Charges

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V =�

i

1

4π�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 #4

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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

4π�0

Q√R2 + z2

Reminders

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•Stay up to date on your textbook reading. You should finish reading Ch. 28, and start on Ch. 29.

•Begin working on HW5.