Ch. 19: Electric charges, Forces, and Fields. (Dr. Andrei Galiautdinov, UGA) 2014FALL - PHYS1112

Transcription

1 Ch. 19: Electric charges, Forces, and Fields (Dr. Andrei Galiautdinov, UGA) 2014FALL - PHYS1112

2 Paper & comb demo 1

3 The most basic electrical phenomenon static electricity The silk handkerchief exhibits a static cling to a cotton shirt in the dryer. The door knob provides a shock after scuffing your feet on the carpet. Sparks fly when you pull the wool sweater off. A lightning strikes during a storm. 2

4 Girl with a balloon 3

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8 Hair up in the air 7

9 What do you think happened here? 8

10 What do you think happened here? 9

11 An important person in the history of the human kind 10

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13 was the balloon rubbed on Donald s hair? 12

14 was the balloon rubbed on Donald s hair? unlikely 13

15 my guess is, these are polarization charges 14

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22 Two balloons 21

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24 Were they charged by rubbing against each other? 23

25 Both balloons are NEGATIVELY charged (must have been charged separately) 24

26 Kids on playground slides 25

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28 Plastic playground slides create enough static to fry hearing implants! Most kids have no problem with the static electricity created from sliding down plastic slides. For children with cochlear implants it's more complicated, though. The static can shut down the cochlear implant instantly. Cochlear implants were first introduced in the 1980s and have always had problems with static electricity. In the beginning, they could be shut down by simply putting on a sweater. Now they are more stable, but they can still shut down with static from slides and balloons. When the cochlear implant is shut down it costs $1,000 to be restored. It can also take days to get it done, leaving the child deaf for days. A company in Missouri that is developing anti-static coating for the Navy is seeing if their product will work on slides. They believe that they could produce it for slides at an affordable price. Metal slides aren t terribly helpful even though they don t produce static, because they get too hot to slide down in warm weather. 27

29 Lightning we ll discuss this later, after introducing the notion of the electric field and the phenomenon of air breakdown 28

30 A bit of history ancient Greeks: 1. Amber (by wool) + feather 2. Magnetite (Fe 2 O 3 ) + iron William Gilbert: Electrification is not limited to amber; it s a general phenomenon Charles Dufay (King of France s gardener): Electrically charged objects can also repel each other Benjamin Franklin: 1. + and electricity 2. Likes repel, opposites attract Charles Coulomb: Inverse-square force law for electricity Hans Oersted: Connection b/w electricity and magnetism (compass needle is deflected by current) Michael Faraday: 1. Concept of E & M fields 2. EM Induction (changing magnetic field produces current in a circuit) James Clerk Maxwell: 1. Laws of E&M in modern form 2. Existence of EM waves 3. Light is an EM wave to 1873 Heinrich Hertz: Produced EM waves in the lab Alexander Popov Guglielmo Marconi: Radio Joseph Thomson: Discovery of the electron P. N. Lebedev: Light pressure E. Rutherford: planetary model of atom Niels Bohr: (semi-) quantum model of atom

31 Charles-Augustin de Coulomb (14 June August 1806) was a French physicist. He is best known for developing Coulomb's law (the inverse-square law of electrostatics). The SI unit of electric charge, the coulomb, was named after him. 30

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33 Unit of charge Name: coulomb [C] Definition (different from the technical SI definition): 1 [C] = charge of (6.242 x ) protons = (6.242 x ) q p, where q p is the basic atomic unit of charge. Thus, q p = x [C] Note: electron charge is q e = (- q p ) = x [C] 32

34 Coulomb s Law Coulomb s law gives the force between two point charges: The force is along the line connecting the charges, and is attractive if the charges are opposite, and repulsive if the charges are like.

35 Coulomb s Law The forces on the two charges are action-reaction forces.

36 Superposition principle If there are multiple point charges, the forces add by superposition.

37 1 [C] is a huge amount of charge. Here s an example: 36

38 1 [C] is a huge amount of charge. Here s an example: 37

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45 The Field Concept (took 2,500 years to arrive at)

46 A bit of history ancient Greeks: 1. Amber (by wool) + feather 2. Magnetite (Fe 2 O 3 ) + iron William Gilbert: Electrification is not limited to amber; it s a general phenomenon Charles Dufay (King of France s gardener): Electrically charged objects can also repel each other Benjamin Franklin: 1. + and electricity 2. Likes repel, opposites attract Charles Coulomb: Inverse-square force law for electricity Hans Oersted: Connection b/w electricity and magnetism (compass needle is deflected by current) Michael Faraday: 1. Concept of E & M fields 2. EM Induction (changing magnetic field produces current in a circuit) James Clerk Maxwell: 1. Laws of E&M in modern form 2. Existence of EM waves 3. Light is an EM wave to 1873 Heinrich Hertz: Produced EM waves in the lab Alexander Popov Guglielmo Marconi: Radio Joseph Thomson: Discovery of the electron P. N. Lebedev: Light pressure E. Rutherford: planetary model of atom Niels Bohr: (semi-) quantum model of atom

47 Michael Faraday (22 September August 1867), one of the most influential scientists in history. Discoveries include: Michael Faraday, H 2 SO 4 The concept of the electromagnetic field Faraday's law of electromagnetic induction Electrochemistry (Faraday's laws of electrolysis; Faraday constant) Chemistry (discovered benzene, invented an early form of the Bunsen burner and the system of oxidation numbers, and popularized terminology such as anode, cathode, electrode, and ion.) Faraday effect (magnetic field causes a rotation of the plane of polarization of light - the first experimental evidence that light and electromagnetism are related) Faraday wheel (which formed the foundation of electric motor technology.) The SI unit of capacitance, the farad, is named in his honor. Albert Einstein kept a picture of Faraday on his study wall, alongside pictures of Isaac 46 Newton and James Clerk Maxwell.

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49 The Field Concept (1) 1) Taken literally, Coulomb s Law describes an Action-at-a-Distance Model of electrostatic interactions in which charges (charged particles) exert forces directly and instantaneously on one another across the distance separating them. Note: these forces act along the lines connecting the charges Symbolically: charge charge 2) This model is good when charges are at rest. 3) Problems arise when charges are allowed to move. Example: - Charge 1 on Earth, charge 2 on Moon. - If charge 1 wiggles (for whatever reason), charge 2 (according to Coulomb) would immediately experience a different force. - This doesn t seem right! - This leads to violation of STR, according to which no influence can propagate faster than the speed of light. 48

50 The Field Concept (2) 1) The Field Model instead imagines that a charge particle creates a field in the space around it, and another particle responds to the field at its own location, not to the first particle directly. Symbolically: charge field charge 2) How does this resolve the problem of moving charges? In our previous example: - When charge 1 is wiggled, it does not directly affect the distant charge 2. - Rather, the wiggling particle wiggles the values of the field in its immediate vicinity. - These wiggles in turn affect the field values at slightly more distant locations, and so on. - The net effect is that ripples in the field move away from the wiggling particle at a finite speed (similar to how ripples on the surface of water do; the difference is, the ripples in the field do not need any medium to propagate in, so they can propagate in a vacuum). - As a result, only when the ripples reach the distant charged particle will it feel a wiggling force.

51 The Field Concept (3) 1) A field, (unlike a particle) exists not at a specific location but throughout space. 2) Even so, the field is a physical object (entity) that (like a particle) has energy, carries momentum, and obeys its own equations of motion. 3) We need a field model b/c instantaneous action at a distance violates STR (no signal can propagate faster than the speed of light). The Field Model naturally resolves this problem. 4) Mathematically, we describe a field (formally) by assigning some kind of numerical quantity to every point in space at every moment in time in our case, vectors. 5) Physically, we define the field (operationally) in terms of what it does in our case, in terms of forces it exerts on charged particles.

52 The Field Concept (4) 1) So, physically, we define the field (operationally) in terms of what it does in our case, in terms of forces it exerts on charged particles. 2) Here s how it works: P Bring in q test and hold it at rest; then measure the force on it. Distribution of charge (regarded as the source of the field at point P). Charges in this distribution are allowed to move arbitrarily. 3) Then, by definition: E F e q test

53 By definition: Translation: E The Field Concept (5) F e q test a) This eq. defines the E-field vector at a point in space & time. b) F e is the electrostatic force experienced at that time by a small test particle with charge q test held at rest at that point in space. c) q test must be small, so that the force it exerts on the charges in the distribution does not push around the charges whose field we are trying to measure. d) E-vector points in the same direction as F e if q test is positive. e) Why divide F e by q test? B/c it is found experimentally that, no matter how source charges move, the force F e the test charge experiences at a given location is proportional to q test itself. So, dividing by q test produces a quantity E that depends only on position relative to the charges creating the field and not on the magnitude of the test charge q test we use. f) Why keep q test at rest? B/c if q test moves (has non-zero velocity) it will experience an additional force (magnetic force) due to motion of the source charges.

54 By definition: Note: E The Field Concept (6) F e q test E-field is a vector quantity, but it is important to remember that it consists of an infinite number of vectors attached to every point in space at any moment in time. To describe the E-field fully you must specify E-vectors everywhere. Unit: [E] = N/C Examples: 1. On a sunny day, due to various atmospheric processes that separate charges, E = 100 to 150 (N/C) 2. During a thunderstorm, E > 10,000 (N/C) 3. When taking a shower, by moving water, E ~ 800 (N/C) 4. In dry air, if E > 3,000,000 (N/C), the air breaks and becomes a conductor, sparks fly.

55 The Field Concept (7) Once the E-field has been determined, we can find the force it exerts on any charged particle by: Note: = qe F e (any charge; limitations apply) F e E (if q > 0) F e E (if q < 0)

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59 Electric field lines.

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63 Electric dipole. 62

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65 Approx. value; found without a calculator. 64

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67 The following is not needed in our class. 66

68 Gauss Law 67

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74 Gauss Law (concepts) 73

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77 E 2 E 1 All of these guesses are wrong! 76

78 E 1 E 2 77

79 Gauss Law (extra slides from previous semester; not really needed) 78

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88 A voltaic pile (~1800) on display in the Tempio Voltiano. 87

89 More slides from previous semester (not really needed) 88

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97 The End 96