1. Chapter 28
Electric Potential
Phys 133 – Chapter 30

2. Looking ahead New force (Chapter 25) New potential energy (Chapter 28)
Phys Chapter 29

3. Electric Potential Energy (Uelec)
Gravitational
Uniform electric field
Point charge
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4. Gravitational potential (energy)
Defined
Then defined
For the gravitational force
Wgrav=(-mg)(∆y)=mg(yi-yf)
∆Ugrav=-Wgrav=mg(yf-yi)
In general
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5. Uniform field: Electric potential energy
where
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6. Uniform field: Electric potential energy
Direction of lower potential energy depends on type of charge
Positive charge
Negative charge
Lower potential energy
Lower potential energy s s
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7. Do Workbook 29.6
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8. Problem 29.3
A proton is released from rest at the positive plate of a parallel plate capacitor. It crosses the capacitor and reaches the negative plate with a speed of 50,000 m/s. What will be the speed if the experiment is repeated with double the amount of charge on the capacitor plates?
(Ans: 7.07x104 m/s)
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9. Electrical Potential Energy of Two Point Charges
where
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10. Question
a) Two point charges (both +Q) have their separation increased. Does the electric potential energy of the system (A) increase, (B) decrease or (C) remain the same?
b) Two point charges (+/- Q) have their separation increased. Does the electric potential energy of the system (A) increase, (B) decrease or (C) remain the same?
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11. Question ans
Like charges
Opposite charges
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12. Do Workbook 29.3
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13. Problem
An electron (q=-e) is sent from very far away towards a charged sphere (Q=-0.25 nC). It gets to a distance of 1.10 mm from the center of the sphere before turning around.
What is the initial speed of the electron?
(Ans: 2.68x107m/s)
What was the speed of the same electron with same initial conditions when it was 2.20 mm away?
e=1.6x10-19C, me=9.1x10-31 kg, K=9x109 Nm2/C2
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14. Problem ans
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15. Electric Potential (Velec)
Gravitational
Uniform electric field
Point charge
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16. Electric Potential (Velec)
Charge creates potential
define
Potential only depends on source charges
Look at
Gravitational
Uniform electric field
Point charge
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17. Gravitational Potential
object
environment
Environment only
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18. Electric potential capacitors
(from before)
object
environment
Environment only
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19. Capacitor: potential representations
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20. Draw V(x) for the two equipotential surfaces
Draw U(x) for a proton in these potentials
Draw U(x) for an electron in these potentials
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21. Workbook 29.18b extension
A proton is at x=0, moving to the right with 5x10-18 J of kinetic energy. What is its kinetic energy at point a?
What if it were an electron?
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22. Workbook 29.18b extension ans
electron
proton
Not enough energy to reach a
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23. Problem Modified
In the figure which capacitor plate, left or right, is the positive plate?
What is the electric potential energy of a proton at the midpoint of the capacitor?
What is the electric field strength inside the capacitor?
In general
What is the electric field strength inside the capacitor in terms of  and o?
What is the electric field strength inside the capacitor in terms of ∆V and d (the distance between the plates?
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24. Only potential difference matters
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25. Electric potential two point charges
(from before)
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26. Point particle: potential representations
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27. Do Workbook 29.21
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28. Electric Potential: multiple charges
No vectors
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29. Do Workbook 29.25
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30. Problem
a) Find an expression for the electric potential V(x,y) for a dipole with point charges +/- Q at y= +/- a.
b) Use the result for the dipole to find the electric potential at x=2 m, y=7 m when a=2 m, and Q=2 nC.
c) What is the potential energy of a proton placed there?
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31. Problem ans r+
y+a
y-a r- x x
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32. Problem plot
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33. Problem ans c) What is the potential energy of a proton placed there?
b) Use the result for the dipole to find the electric potential at x=7 m, y=2 m when a=2 m, and Q=2 nC.
c) What is the potential energy of a proton placed there?
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34. Potential of continuous charge distribution
where
Then let
solve
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35. Problem 29.69
The figure shows a thin rod of length L and charge Q. Find an expression for the electric potential a distance x away from the center of the rod on the axis of the rod.
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36. Problem 29.69 d ith P (d,0) xi ri y x
Sum up contribution from each charge at P x y d
ith
P (d,0) xi ri
Find potential at P due to ith bit of charge
Phys Chapter 29