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I. Electric Charge

I. Electric Charge. Dr. Bill Pezzaglia. Updated 2014Feb03. 2. I. Electric Charge. History of Electricity Coulomb’s Law Electrodynamics. 3. A. History of Electricity. The Electric Effect Charging Methods Measuring Charge. 4. 1a. Thales of Miletos (624-454 BC).

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I. Electric Charge

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  1. I. Electric Charge Dr. Bill Pezzaglia Updated 2014Feb03

  2. 2 I. Electric Charge • History of Electricity • Coulomb’s Law • Electrodynamics

  3. 3 A. History of Electricity • The Electric Effect • Charging Methods • Measuring Charge

  4. 4 1a. Thales of Miletos (624-454 BC) • Famous theorems of similar triangles • Amber rubbed with fur attracts straw • “Amber” in greek:  “elektron” Here is a narrow tomb Great Thales lies; yet his renown for wisdom reached the skies

  5. 5 1.b. William Gilbert (1544-1603) • “Father of Science” (i.e. use experiments instead of citing ancient authority) • 1600 Book “De Magnete” • Originates term “electricity” • Distinguishes between electric and magnetic force • Influences Kepler & Galileo • Glass rubbed with Silk attracts objects • Invented “Versorium” (needle) used to measure electric force

  6. 6 1.c. Stephen Gray (1696-1736)[student of Newton!] • 1729 does experiment showing electric effects can travel over great distance through a thread or wire. • Classifies Materials as: • Conductors: which can remove charge from a body • Insulators: that do not.

  7. 7 + + + - 1.d. Charles Dufay (1689-1739) • 1733 Proposes “two fluid” theory of electricity • Vitreous (glass, fur) (+) • Resinous (amber, silk) (-) • Summarizes Electric Laws • Like fluids repel • opposite attract • All bodies except metals can be charged by friction • All bodies can be charged by “influence” (induction)

  8. 8 1.e. Benjamin Franklin (1706-1790) • 1752 Kite Experiment proves lightening is electric • Proposes single fluid but two state model of charge • + is an excess of charge • - is deficit in charge • Charge is conserved (objects are naturally neutral)

  9. 9 2. Methods of Charging Three basic methods • Triboelectric (friction) • Conduction • Induction (Influence)

  10. + 10 2.a.1 Triboelectrification chart Franklin and others contributed to determining the relative charge obtained by rubbing objects together. For example, amber on fur will give negative to amber, and plus to fur Dry human skin Asbestos Leather Rabbit's fur Glass Mica Human hair Nylon Wool Lead Cat's fur Silk Aluminum Paper (Small positive charge) Cotton (No charge) Steel (No charge) Wood (Small negative charge) Amber Sealing wax Rubber balloon Resins Hard rubber Nickel, Copper Sulfur Brass, Silver Gold, Platinum Synthetic rubber Polyester Styrene (Styrofoam) Saran wrap Polyethylene (like Scotch tape) Vinyl (PVC) Silicon Teflon 0 -

  11. 11 2.a.2 Otto von Guericke 1602 - 1686 • 1650 Invents Vacuum Pump (famous Magdeburg spheres that horses could not pull apart) • 1660 Invents static electricity generator, a large sulfur ball mounted on a pole inside a glass globe. The sulfur ball was rotated by a hand crank. The rotating ball rubbed against a pad generating static electricity sparks

  12. 12 2.a.3 Van Marum Machine (1784) The biggest tribo- electrostatic generator ever built, could produce voltage with any polarity.

  13. 13 2.a.4 Van der Graaf Generator (1929)

  14. 14 ++ ++ ++ ++ 2.b. Charge by Conduction If an uncharged conductor touches a charged one, the charge will be shared. When separated, they will both now have charge

  15. 15 2.c.1 Charge by Induction Aka chargeby “influence” (First done by 1759  -  Francis Ulrich Theodore Aepinus ?)

  16. 16 2.c.2 Charge by Induction Another way of doing it that is exploited by electrostatic generators

  17. 17 2.c.3 Electrophorus (1775) Invented by Alessandro Volta (1745-1827)(also invents the battery in 1800 ) Uses method of induction to create charge

  18. 18 2.c.4 Wimshurst Machine (1880) Invented by James Wimshurst (1832 – 1903) Two disks rotate in opposite directions, mutually inducing charge

  19. 19 3. Measurement of Charging Without really knowing what IS charge, how was it measured? (a) 1753 John Canton (1718-1772) Suggests deflection angle of Pith Balls is a measure of charge.

  20. 20 3b Henley’s Electrometer • 1770 First quantitative device. Deflection angle measures charge (its not however linear. Why?)

  21. 21 3c Electroscope • 1786 Gold Leaf Electroscope invented by Abraham Bennet (1750 - 1799) • 1887 Braun Electroscope is less sensitive, but more accurate

  22. 22 B. Coulomb’s Law • The Inverse Square Law • Coulomb’s Law • Units of Charge

  23. 23 B1. The Inverse Square Law (a) Alkindus (al-Kindi 801-873), Based upon optics of Euclid, knew that light rays are scattered in a cone with the light source as apex, hence PROBABLY knew that the intensity of light drops off in proportion to the increase in the surface area (i.e. square of the distance)

  24. 24 3a. Inverse Square Law

  25. 25 3b. Inverse Square Law • Apparent Luminosity drops off inversely proportional to squared distance. • Sun at Jupiter (5x further away than earth) would appear 1/25 as bright. • Kepler knew this • Gravity and Coulomb’s law behave similarly, so is there a connection?

  26. B1b. Johannes Kepler (1571-1630) 26 • Laws of Planetary Motion • 1605 first two laws • 1609 third law • In his writings, it is clear that the inverse square law for intensity of light (e.g. from the sun, and planets) was well known at the time. • He argues that planetary force does NOT follow the same law as light

  27. 27 B1c. Review: Gravity obeys inverse square law • 1666 probably derived first 3 laws • Law of Gravity probably done around the same time • 1687 He didn’t publish his work for some 20 years until Halley twisted his arm (Halley paid for it!) • Law of Gravity has inverse square law built into it. Newton 1643-1727 Force due to gravity = G is the “gravitational constant”, measured 100 years later by Cavendish: G=6.67x10-11 Nm2/kg2

  28. 28 B2. Coulomb’s Law It is found that electric force obeys a law completely analogous to the law of gravity. Except: • Gravity attracts, while like charges repel • Plus & Minus charge, while there is only Plus mass* *antimatter has positive mass

  29. 29 B2.a Joseph Priestley (1733-1804) • Friend of Franklin • 1760-6 He shows there is no electric force inside a charged hollow conductor. • He argues this is analogous to Newton showing there is no gravitational force inside a hollow mass shell • By Analogy, argues electric force obeys inverse square law.

  30. 30 B2.b Henry Cavendish (1731-1810) • 1797 using a “torsion balance” measures the density of the earth (which leads to a value for the gravitational constant “G”). • Torsion Balance was invented by John Michell, but he died before the experiment could be done, and so the equipment was obtained by Cavendish. • 1772 little known fact that Cavendish determined that electric forces obey the inverse square law (cited by Maxwell), using charges on concentric spheres

  31. 31 B2.c: Coulomb’s Law • Charles-Augustin de Coulomb 1736-1806 • 1785 using a “torsion balance” measures the inverse square law between charges. “q” is measure of charge k= “Coulomb constant”

  32. 32 This dial allows you to adjust and measure the torque in the fibre and thus the force restraining the charge This scale allows you to read the separation of the charges Coulomb's Torsion Balance

  33. 33 B2.c Charles-Augustin de Coulomb (1736-1806) • 1785 using a “torsion balance” measures the inverse square law between charges. • F = qq’/r2 • 1 dyne of forceat 1 cm distanceif charges are1 “statCoulomb”(aka esu)

  34. 34 B3. Units of Charge • 1833 Gauss shows all mechanical units can be written in terms of base units of mass, length and time. • 1854 Wilhelm Weber shows that all electromagnetic units can be defined by including one more base unit (for charge or current)

  35. 35 B3a. “Old” Electrostatic Units • Old Unit: esu or “electrostatic unit” or “statCoulomb” is unit of charge such that two 1 esu charges separated by 1 cm exert force of 1 dyne (cgs system of units!). • Coulomb Law is simple: F = qq’/r2 • Problem: can’t relate it easily to magnetic units

  36. 36 B3b. The Coulomb Unit • 1861 Joule, Kelvin & Maxwell define unit of resistance, from which other electrical units can be defined (a column of 106 cm of mercury with 1mm x 1mm cross section at 0° C has resistance of 1 ohm). This was a cgs system. • 1881 units of Coulomb (and Amp) defined in mks (SI) system. • Coulomb is amount of charge deposited by 1 amp in 1 second • Amp is amount of current that delivers 1 Watt of energy passing through 1 ohm of resistance.

  37. 37 B3c. Permittivity of Space • SI Unit of charge is “Coulomb” “C” • Coulomb Constant: k=8.988x109 Nm2/C2 • Permittivity of free space defined: k=1/4o • o= 8.85x10-12 C2/Nm2 Or: force between 1 coulomb charges 1 meter apart is about 9 billion newtons. Constant “k” is analogous to the Cavendish constant “G” in Newton’s gravity law.

  38. 38 B3d. Fundamental Charge • Smallest charge in nature is: e=1.67x10-19 coulombs • This is the charge on the proton, and negative this is the charge on the electron. • The universe appears to be electrically neutral. We don’t know why its almost all matter, and hardly any antimatter.

  39. 39 C. Electrodynamics Rough Draft (Notes on Board) • The Superposition Principle • Force from Discrete Charges • Force from Continuous Charges

  40. 40 C1. Electric Force & Newton’s Laws • Electrical forces cause acceleration (Newton’s 2nd law)kq1q2/r2=F=m1a • Point Mass Theorem: The force from a sphere of uniform charge is the same as the force from a point charge concentrated at the center of the sphere • Extended Body: The electrical force on an extended body is equivalent to the total force applied to all the mass concentrated at the center of mass.

  41. 41 C2. Electric Force is a VECTOR • Vectors have magnitude and direction • Electrical Force is a “central force”, the force is directed along the line between their centers, represented by vector “r”.

  42. 42 C3.a Superposition Principle & Galileo • Galileo: If a body is subjected to two separate influences, each producing a characteristic type of motion, it responds to each without modifying its response to the other. • In projectile motion, for example, the horizontal motion is independent of the vertical motion. • Linear Superposition of Velocities: The total motion is the vector sum of horizontal and vertical motions. Galileo 1564-1642

  43. 43 C3.b Sir Isaac Newton(1643-1727) • 1666 Newton’s Second Law:ma = sum of forces acting on the mass • Today we know it’s the VECTOR SUM of the forces that we use here, i.e. linear superposition • But in 1666 it was more than 100 years before the idea of a vector (more like 170 years)! Newton added forces using geometric arguments.

  44. 44 C3.c Superposition is adding vectors • 1753 Bernoulli expresses “Superposition principle” • 1843 Möbius presents parallelogram rule for adding forces (i.e. vector-like quantities). • 1843 Hamilton invents modern concept of 3D “vector” • 1880 Gibbs invents modern system of vectors we now use

  45. 45 C3.d Force from Many Discrete Charges Lecture Notes In Class Essentially the electric force on a certain point charge is the superposition of the forces from all the other charges. Lots of “Vector Addition” Here

  46. 46 References • Build simple electrophorus http://www.exploratorium.edu/snacks/charge_carry.html • Multimedia animations http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/index.html • In particular, static electricity animations at • http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/index.html#estatics • Make an electroscope http://www.mos.org/sln/toe/simpleelectroscope.html • More on electroscopes: http://www.sparkmuseum.com/ELECTROSCOPE.HTM • Leyden Jars: http://www.sparkmuseum.com/LEYDEN.HTM • http://www.sizes.com/units/ohm.htm

  47. 47 Things to Do • Finish C3 • Find tesla museum stuff • Source of word “electrode”

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