Lesson 1 Stationary Point Charges and Their Forces

1. Lesson 1Stationary Point Charges and Their Forces

2. Today we will: • learn the basic characteristics of the electrostatic force • review the properties of conductors and insulators • learn what is meant by “electrostatic induction” • find out why static electrostatic forces are usually attractive • discuss the problem of force at a distance • learn the basics of two types of models that explain • why there are forces Class 2

3. Basic Rules of Electrostatics Charges come in two types: positive and negative. Positive charge is produced on a glass rod by rubbing it with silk or plastic. Negative charge is produced on a rubber rod by rubbing it with fur. Like charges repel, unlike charges attract.

4. Basic Rules of Electrostatics Conductors are materials in which charges move freely. Insulators are materials in which charges remain in fixed locations. Charges come in multiples of the electric charge. The total charge in the universe is always conserved. The force between charges is stronger when the charges are closer.

5. What happens when we put a charged rod near a stream of water?

6. Conclusion: The stream of water is attracted both rods. It doesn’t matter if the rod is positively charged or negatively charged.How can we understand this?

7. Polarization • In most neutral atoms or molecules, the center of positive charge coincides with the center of negative charge • In the presence of a charged object, these centers may separate or rotate slightly • This results in more positive charge on one side of the molecule than on the other side • This realignment of charge on the surface of an insulator is known as polarization

8. Examples of Polarization • The charged object (on the left) induces charge on the surface of the insulator • A charged comb attracts bits of paper due to polarization of the paper

9. Examples of Polarization • The force between the objects is attractive because the force is stronger between closer charges.

10. How does an electrophorus work? +++++++++++++++++++++++++++++++++++++++++++++++++++

11. Charges in the conducting plate become polarized.Charges on the insulating plate remain where they were. +++++++++++++++++++++++++++++++++++++++++++++++++++ −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− +++++++++++++++++++++++++++++++++++++++++++++++++++

12. Electrons from your finger flow into the plate, neutralizing the top surface. −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− +++++++++++++++++++++++++++++++++++++++++++++++++++

13. Negative charge redistributes itself on the metal plate. − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − −

14. When you touch it again, electrons flow off the plate into your finger.

15. Physics and Truth As physicists, we deal with models. Models require 1) symbols and 2) rules for manipulating symbols. These symbols and rules have a 1-to-1 correspondence with nature. Physicists can say relatively little about truth at a fundamental level.

16. … So is light a wave or a particle? sometimes it acts like a wave sometimes it acts like a particle light is neither wave nor particle -- it’s light.

17. Action at a distance. action = force If the earth is 93,000,000 miles from the sun, how does it know it should be attracted to the sun?

18. Action at a distance. We frequently use two very different models or theories to explain action at a distance. Remember that both are models, and neither is “truth.”

19. Virtual Particle Theories charges constantly emit and reabsorb virtual particles that carry energy and momentum. if another charge absorbs the virtual particle, a force is exerted.

20. Virtual Particle Theories

21. Virtual Particle Theories electromagnetic force: QED quantum electrodynamics +weak force: electroweak theory strong force: QCD quantum chromodynamics

22. Geometrical Theories matter modifies the curvature of space-time. curved space-time affects the motion of matter.

23. Geometrical Theories gravity: General Relativity + electromagnetic force: KK Kaluza-Klein Theories – in 5-dimensional space.

24. Three Models of Electromagnetic Forces Thread Model: Describes the interactions between point charges. Tells why forces behave as they do. Field Lines: Easy way to visualize forces between collections of charges. Maxwell’s Equations: A mathematical version of field lines.

25. Today we will: • learn how the thread model describes the force between • point charges at rest • construct Coulomb’s law from the thread model • learn how to use Coulomb’s law to calculate the force • between charges at rest Class 3

26. Thread Model valid except in quantum mechanical regime. helps us understand the relationship between electricity and magnetism. gives quantitative results. useful for visualizing forces, radiation, magnetic fields.

27. Field particle Feels force Thread Model Source particle Causes force

28. Field particle Feels force Thread Model Source particle Causes force We will only draw the threads of the source charge!

29. When a source particle is at rest, it emits threads isotropically and in huge numbers. Threads have a head (solid circle) and a tail (open circle). Thread Model http://www.physics.byu.edu/faculty/rees/220/AVIfiles/StatThreads.avi

30. + Threads are very short. Threads travel at the speed of light radially outward. Thread Model

31. – Threads point away from positive sources and toward negative sources. Threads are not modified by the presence of charges. Thread Model

32. Remember that the threads always travel radially outward! Thread Model http://www.physics.byu.edu/faculty/rees/220/AVIfiles/plusminusL.avi

33. Force Thread Model • To find the force on a charge embedded in a sea of threads, all we need to do is look at a snapshot threads. • If the charge is positive, the force is in the direction of the threads. • It doesn’t matter how the threads are moving!

34. Thread Model Force • If the charge is negative, the force is opposite the direction of the threads.

35. source charges field charges Force + + Force + – Force – + Force – – Thread Model • The force on positive field charges is in the direction of the threads. • The force on negative field charges is opposite the direction of the threads.

36. Thread Model Threads carry no energy or momentum. They exert a force by modifying space near a field particle. To calculate the force on a field particle, we need to know: The charge of the field particle. The density of threads near the field particle. The length of the threads. The direction of the threads.

37. Thread Model

38. Thread Model constants

39. Thread Model charge of the field particle

40. Thread Model thread vector: gives the length and direction of the threads

41. Thread Model thread density: gives the number of threads per unit volume

42. Finding the Force We know everything but ν(nu), the density of threads. But if we know how many threads are emitted per second, we can determine how many threads there are per unit volume anywhere in space!

43. dr0 r0 The Number of Threads in a Shell In the text, we found the number of threads in a spherical shell and the volume of the shell. Dividing these gives us the density.

44. Coulomb’s Law

45. In practice, it’s easier to change this just a little: Coulomb’s Law

46. A Short Vector Review A θ • Magnitude = A, direction = θ • Unit vectors: • Components:

47. A Short Vector Review A θ B • Dot product: • Cross product:

48. Finding the Force To calculate a force, we need: ε0is a constant qs is the charge of the source particle– usually given qfis the charge of the field particle– usually given is the vector from the source to the field particle

49. +3C (2m, 3m) An example: −4C (7m, 1m) Red: at (2m, 3m), charge is +3C. Blue: at (7m, 1m), charge is −4C. What is the force on the blue charge?

50. If you put everything in SI units → The result is in SI units! Rule for Units