1. Electric Charge, Force, and Energy
Prepared by
Dedra Demaree, Georgetown University
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2. Electrostatic and Coulombs Law review
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3. Summary
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4. Summary
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5. Summary
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6. 14.4 Coulombs Force Law
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7. Coulomb's law
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8. Example 14.5
Metal spheres on insulating stands have the following electric charges: qA = +2.0 x 10–9 C, qB = +2.0 x 10–9 C, and qC = –4.0 x 10–9 C. The spheres are placed at the corners of an equilateral triangle whose sides have length d = 1.0 m, with qC at the top of the triangle. What is the magnitude of the total (net) electric force that spheres A and B exert on sphere C?
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9. 14.5 Electrical Potential Energy
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10. Electric potential energy: A qualitative analysis
A positively charged cannonball is held near another fixed positively charged object in the barrel of the cannon.
Some type of energy must decrease if gravitational and kinetic energies increase in this process.
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11. Zero Level assignment for U
During this discussion on Electrical potential Energy (Uq) remember we make a Zero-level assignment for potential energy (just like Ug)
I.e… When 2 objects are so far apart they essentially do not interact Potential Energy (Uq)
However: Ug only pulled Uq can push and pull
So “+” & “-” charge: Positive Potential energy when together 0 at ∞.
So “+” & “+”, or “-” & “-” charge Uq Is negative when touching and 0 at ∞.
Ug when objects are touching “-” Uq is negative when touching and 0 at ∞, just like a same charge interactions.
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12. Zero Level assignment for U
The zero assignment is due to Work and the displacement vector.
Take an object away from earth you must do + work on the system but Fgrav does negative work (Fgrav opposite of the displacement)
Like Charge. You must do work to pull apart (positive work) but Uq is negative because the Fq vector is in the opposite direction
Opposite charge. Pull object apart (Positive Work) Uq is positive because the Work due to the Fq is positive because its in the same direction as the displacement
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13. Electric potential energy: A qualitative analysis
Consider two oppositely charged blocks, one of which can slide without friction. When the negatively charged block is released and moves nearer the nut, the kinetic energy of the system increases.
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14. Electric potential energy: A quantitative analysis
Use the generalized work-energy principle to analyze a situation where only the electric potential energy changes when work is done.
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15. Derivation of ∆Uq
If we keep ∆r small we can look at changes through small displacements. As we get closer to q1 it takes a larger force…Work required to push q2 toward q1 there must increases as we get closer to q1.
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16. = Derivation of ∆Uq 𝑊=𝑘 𝑞 1 𝑞 2 ( 1 𝑟 𝑓 − 1 𝑟 𝑖 )
At each step of the process
no accelera­tion and therefore no change in kinetic energy or any other kind of energy.
Only energy change of the system due to this work is the electric potential energy change.
By substituting the above expression for W into the work energy theorem, and zeros for all energy changes except the electric poten­tial energy change, we find
𝑊=𝑘 𝑞 1 𝑞 2 ( 1 𝑟 𝑓 − 1 𝑟 𝑖 )
(Ki + Ugi +Usi + Uqi) + W = (Kf +Ugf + Usf + Uqf) +∆Uint =
r = distance between the objects

17. Electric potential energy
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18. Tip
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19. Example 14.6
Two oppositely charged objects (with positive charge +q and negative charge –q) are separated by distance ri. Will the electric potential energy of the system decrease or increase if you pull the objects farther apart? Explain.
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20. Graphing the electric potential energy versus distance
Because of the 1/r dependence, the electric potential energy approaches positive infinity when the separation approaches zero, and it becomes less positive and approaches zero as like charges are moved far apart.
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21. Graphing the electric potential energy versus distance
Because of the 1/r dependence, the electric potential energy approaches positive infinity when the separation approaches zero, and it becomes less positive and approaches zero as like charges are moved far apart.
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22. Electric potential energy of multiple charge systems
Each pair of charged objects has an associated electric potential energy, and the total electric potential energy of the system is the sum of the energies of all pairs.
Energy is NOT A VECTOR SO JUST ADD THEM UP (KEEP TRACK OF NEGATIVE AND POSITIVES) (i.e. not coulombs law where we must add VECTORS)
For three charged objects, the total electric potential energy is:
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23. 14.6 Skills for Fq (Coulombs law) and Uq (Energy) Problems
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24. Skills for analyzing processes involving electric force and electric potential energy
In conjunction with your problem-solving strategy:
Decide whether you can consider the charged objects to be point-like.
If you are using the work-energy principle, construct an energy bar chart. Decide where the zeros for potential energies are.
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25. Example 14.8
Suppose that a radon atom in the air in a home is inhaled into the lungs. While in the lungs, the nucleus of the radon atom undergoes radioactive decay, emitting an α (alpha) particle, which is composed of two protons and two neutrons. During this process, the radon nucleus turns into a polonium nucleus with charge +84e and mass 3.6 x 10–25 kg. The α particle has charge +2e and mass 6.6 x 10–27 kg. Suppose the two particles are initially separated by 1.0 x 10–15 m and are at rest. How fast is the α particle moving when it is very far from the polonium nucleus?
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26. 14.8 Putting it All Together
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27. Van de Graaff generator
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28. Van de Graaff generator
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29. Van de Graaff generator
Large Uq between the dome/ground system
Charge can accumulate on the dome up to 10-5 C (This is a
big charge)
If you hold a grounded metal ball about 10 cm from the doom you get a
flash and cracking sound.
What happens:
Cosmic rays, high energy particles coming from space continuously rain down on Earth’s atmosphere from space.
These rays ionize atoms, producing free electrons and positively charged ions in the Earths atmosphere.
Positive dome attracts the free electrons present in the air.
The attraction causes the electrons to accelerate to the dome.
e- collide with other particles causing more ionizations.
Many of the free e- will then recombine with atoms,
Light is produced and we see a spark (Must reduce energy when combining this cause a light photon more on this later in the class)
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30. Example 14.10
The energy needed to remove an electron from a hydrogen atom is approximately 2 x 10–18 J (about the same for other atoms, too). The average distance a free electron in air will travel between collisions, called the mean free path, is about 10–6 m. The dome has a 0.15 m radius and a +10–5 C charge. Could a free electron in the air gain enough kinetic energy to ionize an atom and cause a spark as it travels that short distance toward the charged dome?
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31. Wimshurst machine
The Wimshurst, invented in the 1880s, consists of two plastic disks that rotate in opposite directions. It can produce large charge separations.
One of the electrodes becomes positively charged and the other becomes negatively charged.
When the two electrodes are brought near one another, we see sparks as long as 5-10 cm.
The Wimshurst machine not only allows us to create large charges on the electrodes but also allows us to study the creation of the spark and its dependence on the distance between the electrodes—one goal of the next chapter.
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32. Summary
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33. Summary
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34. Summary
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35. Summary
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36. Summary
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