1. Chapter 21
Electric Potential

2. 21 Electric Potential
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6. Example Problem
Answers for a positive test charge: a) 0; b) negative; c) positive; d) negative; e) zero; f) negative; g) zero (Instructor should state whether moving charge is positive, negative, or zero.)
Is the change ∆U of the particle positive, negative, or zero as it moves from i to f?
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7. Electric Potential Energy
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8. Electric Potential
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9. Conceptual Example Problem
d) 1 = 2, 3 = 4
e) 1, 2, 3
Rank in order, from largest to smallest, the electric potentials at the numbered points.
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10. Charged Particle Moving Through a Potential Difference
b) 3, 1 = 2
c) 3, 2, 1
d) 1 = 2, 3 = 4
e) 1, 2, 3
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12. Example Problem
A proton has a speed of 3.5 x 105 m/s at a point where the electrical potential is 600 V. It moves through a point where the electric potential is 1000 V. What is its speed at this second point?
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13. A Topographic Map
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14. Graphical Representations of Electric Potential
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15. Example Problem
A proton is released from rest at point a. It then travels past point b. What is its speed at point b?
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16. Potential of a Parallel-Plate Capacitor
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17. The Potential Inside a Parallel-Plate Capacitor
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18. Example Problem
A parallel-plate capacitor is held at a potential difference of 250 V. A proton is fired toward a small hole in the negative plate with a speed of 3.0 x 105 m/s. What is its speed when it emerges through the hole in the positive plate? (Hint: The electric potential outside of a parallel-plate capacitor is zero).
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19. Electric Potential of a Point Charge
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20. Electric Potential: Charged Sphere
Outside of a sphere of charge Q the potential has the same form as for a point charge Q:
If the sphere has radius R and the potential at its surface is V0, then the potential a distance r from its center can also be written
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21. Example Problem For the situation shown in the figure, find
The potential at points a and b.The potential difference between a and b.
The potential energy of a proton at a and b.
The speed at point b of a proton that was moving to the right at point a with a speed of 4.0 x 105 m/s.
The speed at point a of a proton that was moving to the left at point b with a speed of 4.0 x 105 m/s.
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22. Example Problem A 2.0-mm-diameter plastic bead is charged to –1.0 nC.
A proton is fired at the bead from far away with a speed of 1.0 x 106 m/s, and it collides head-on. What is the impact speed?
An electron is fired at the bead from far away. It “reflects,” with a turning point 0.10 mm from the surface of the bead. What was the electron’s initial speed?
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23. Connecting Potential and Field
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24. Potential and Field for Three Important Cases
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25. Example Problem Source charges create the electric potential shown.
What is the potential at point A? At which point, A, B, or C, does the electric field have its largest magnitude?
Is the magnitude of the electric field at A greater than, equal to, or less than at point D?
What is the approximate magnitude of the electric field at point C?
What is the approximate direction of the electric field at point C?
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26. A Conductor in Electrostatic Equilibrium
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27. Example Problem
What is Q2?
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28. Capacitance and Capacitors
The charge ±Q on each electrode is proportional to the potential difference ∆VC between the electrodes:
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29. Charging a Capacitor
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30. The Capacitance of a Parallel-Plate Capacitor
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31. Dielectrics and Capacitors
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32. Dielectric Constant
With a dielectric between its plates, the capacitance of a parallel-plate capacitor is increased by a factor of the dielectric constant κ:
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33. Summary
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34. Summary
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