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I. Electric Charge I 2 I. Electric Charge I. Electric Charge A. History of Electricity Dr. Bill Pezzaglia B. Coulomb’s Law C. Electrodynamics Updated 2014Feb03 3 1a. Thales of Miletos (624-454 BC) 4 A. History of Electricity • Famous theorems of similar triangles 1) The Electric Effect • Amber rubbed with fur attracts straw 2) Charging Methods • “Amber” in greek: “elektron” 3) Measuring Charge Here is a narrow tomb Great Thales lies; yet his renown for wisdom reached the skies 5 6 1.b. William Gilbert (1544-1603) 1.c. Stephen Gray (1696-1736) [student of Newton!] •“Father of Science” (i.e. use experiments instead of citing ancient authority) • 1729 does experiment showing electric effects can •1600 Book “De Magnete” travel over great distance – Originates term “electricity” through a thread or wire. – Distinguishes between electric and magnetic force – Influences Kepler & Galileo • Classifies Materials as: – Glass rubbed with Silk attracts – Conductors: which can objects remove charge from a body – Insulators: that do not. •Invented “Versorium” (needle) used to measure electric force 1 7 8 1.d. Charles Dufay (1689-1739) 1.e. Benjamin Franklin (1706-1790) •1733 Proposes “two fluid” theory of electricity •1752 Kite Experiment proves lightening is electric – Vitreous (glass, fur) (+) – Resinous (amber, silk) (-) •Proposes single fluid but two state model of charge •Summarizes Electric Laws + + – Like fluids repel + is an excess of charge – opposite attract + - - is deficit in charge – All bodies except metals can be charged by friction – All bodies can be charged by “influence” (induction) •Charge is conserved (objects are naturally neutral) 9 Dry human skin 10 + Asbestos 2.a.1 Triboelectrification chart Leather 2. Methods of Charging Rabbit's fur Glass Mica Human hair Nylon Franklin and others contributed Wool Three basic methods Lead to determining the relative Cat's fur Silk charge obtained by rubbing Aluminum Paper (Small positive charge) objects together. Cotton (No charge) 0 Steel (No charge) a) Triboelectric (friction) Wood (Small negative charge) Amber For example, amber on fur will Sealing wax Rubber balloon give negative to amber, and Resins Hard rubber plus to fur Nickel, Copper Sulfur b) Conduction Brass, Silver Gold, Platinum Synthetic rubber Polyester Styrene (Styrofoam) Saran wrap Polyethylene (like Scotch tape) c) Induction (Influence) Vinyl (PVC) Silicon - Teflon 11 12 2.a.2 Otto von Guericke 1602 - 1686 2.a.3 Van Marum Machine (1784) •1650 Invents Vacuum Pump The biggest tribo- (famous Magdeburg spheres that horses could not pull apart) electrostatic generator ever •1660 Invents static electricity generator, a large sulfur ball built, could mounted on a pole inside a glass produce voltage globe. The sulfur ball was rotated by a hand crank. The rotating ball with any polarity. rubbed against a pad generating static electricity sparks 2 13 14 2.a.4 Van der Graaf Generator (1929) 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 16 2.c.1 Charge by Induction 2.c.2 Charge by Induction Aka charge Another way of by “influence” doing it that is (First done by exploited by 1759 - Francis Ulrich Theodore electrostatic Aepinus ?) generators 17 18 2.c.3 Electrophorus (1775) 2.c.4 Wimshurst Machine (1880) Invented by Alessandro Volta (1745-1827) Invented by James Wimshurst (1832 – 1903) (also invents the battery in 1800 ) Two disks rotate in opposite directions, mutually inducing charge Uses method of induction to create charge 3 19 20 3. Measurement of Charging 3b Henley’s Electrometer Without really knowing what IS charge, •1770 First quantitative how was it measured? device. Deflection angle measures charge (its not (a) 1753 John Canton however linear. Why?) (1718-1772) Suggests deflection angle of Pith Balls is a measure of charge. 3c Electroscope 21 22 B. Coulomb’s Law •1786 Gold Leaf Electroscope invented by Abraham Bennet (1750 - 1799) 1) The Inverse Square Law •1887 Braun Electroscope is less sensitive, but more accurate 2) Coulomb’s Law 3) Units of Charge 23 24 B1. The Inverse Square Law 3a. 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) 4 3b. Inverse Square Law 25 B1b. Johannes Kepler (1571-1630) 26 •Apparent Luminosity drops off inversely proportional to squared distance. •Laws of Planetary Motion •1605 first two laws •Sun at Jupiter (5x further away than earth) would •1609 third law appear 1/25 as bright. •In his writings, it is clear that •Kepler knew this the inverse square law for •Gravity and intensity of light (e.g. from Coulomb’s law the sun, and planets) was well behave similarly, so is known at the time. there a connection? •He argues that planetary force does NOT follow the same law as light B1c. Review: Gravity obeys inverse square law 27 28 • 1666 probably derived first 3 laws B2. Coulomb’s Law • Law of Gravity probably done around the same time It is found that electric force obeys a law • 1687 He didn’t publish his work for some 20 years until Halley twisted his arm completely analogous to the law of (Halley paid for it!) gravity. • Law of Gravity has inverse square law built into it. Except: Newton 1643-1727 • Gravity attracts, while like charges repel Force due to gravity = GM1 M 2 F 2 • Plus & Minus charge, while there is R only Plus mass* G is the “gravitational constant”, measured 100 years -11 2 2 later by Cavendish: G=6.67x10 Nm /kg *antimatter has positive mass B2.a Joseph Priestley (1733-1804) 29 B2.b Henry Cavendish (1731-1810) 30 • Friend of Franklin • 1797 using a “torsion balance” measures the density of the earth • 1760-6 He shows there is no (which leads to a value for the electric force inside a charged gravitational constant “G”). hollow conductor. • Torsion Balance was invented by • He argues this is analogous to John Michell, but he died before the Newton showing there is no experiment could be done, and so gravitational force inside a the equipment was obtained by Cavendish. hollow mass shell • By Analogy, argues electric • 1772 little known fact that force obeys inverse square Cavendish determined that electric forces obey the inverse square law law. (cited by Maxwell), using charges on concentric spheres 5 B2.c: Coulomb’s Law 31 32 • Charles-Augustin de Coulomb 1736-1806 Coulomb's Torsion Balance • 1785 using a “torsion balance” measures the inverse square This dial allows you to adjust and law between charges. measure the torque in the fibre and thus the force restraining the q q charge F k 1 2 R2 “q” is measure of charge k= “Coulomb constant” This scale allows you to read the separation of the charges 33 34 B2.c Charles-Augustin de Coulomb (1736-1806) B3. Units of Charge • 1785 using a “torsion balance” measures the inverse square law between charges. • 1833 Gauss shows all mechanical units can be written in terms of base units of mass, • F = qq’/r2 length and time. • 1 dyne of force • 1854 Wilhelm Weber shows that at 1 cm distance all electromagnetic units can be if charges are defined by including one more 1 “statCoulomb” base unit (for charge or current) (aka esu) 35 36 B3a. “Old” Electrostatic Units B3b. The Coulomb Unit • 1861 Joule, Kelvin & Maxwell define unit of resistance, • Old Unit: esu or “electrostatic unit” or from which other electrical units can be defined (a “statCoulomb” is unit of charge such that two column of 106 cm of mercury with 1mm x 1mm cross 1 esu charges separated by 1 cm exert force of section at 0° C has resistance of 1 ohm). This was a 1 dyne (cgs system of units!). cgs system. • 1881 units of Coulomb (and Amp) defined in mks (SI) • Coulomb Law is simple: F = qq’/r2 system. • Coulomb is amount of charge deposited by 1 amp in 1 second • Problem: can’t relate it easily to magnetic units •Ampis amount of current that delivers 1 Watt of energy passing through 1 ohm of resistance. 6 37 38 B3c. Permittivity of Space B3d. Fundamental Charge • SI Unit of charge is “Coulomb” “C” • Smallest charge in nature is: • Coulomb Constant: k=8.988x109 Nm2/C2 e=1.67x10-19 coulombs • Permittivity of free space defined: k=1/4 o • This is the charge on the proton, and -12 2 2 • o= 8.85x10 C /Nm negative this is the charge on the q q q q electron. F k 1 2 1 2 R2 4 R2 • The universe appears to be electrically 0 neutral. We don’t know why its almost all 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. matter, and hardly any antimatter. 39 C1. Electric Force & Newton’s Laws 40 C. Electrodynamics • Electrical forces cause acceleration (Newton’s 2nd law) Rough Draft (Notes on Board) 2 kq1q2/r =F=m1a 1) The Superposition Principle • 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 2) Force from Discrete Charges sphere • Extended Body: The electrical force on an 3) Force from Continuous Charges extended body is equivalent to the total force applied to all the mass concentrated at the center of mass. C2. Electric Force is a VECTOR 41 C3.a Superposition Principle & Galileo 42 • Vectors have magnitude and direction • Galileo: If a body is subjected to two separate influences, each ˆ ˆ ˆ producing a characteristic type of F (Fx , Fy , Fz ) Fxi Fy j Fz k motion, it responds to each without modifying its response to the • Electrical Force is a “central force”, the force is other.
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