I. Electric Charge. I. Electric Charge. A. History of Electricity. B. Coulomb s Law. C. Superposition. 1a. Thales of Miletos ( BC)

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1 I. Electric Charge I. Electric Charge 2 A. History of Electricity Dr. Bill Pezzaglia B. Coulomb s Law C. Superposition Updated 26Jan2010 A. History of Electricity 3 1a. Thales of Miletos ( BC) 4 1) The Electric Effect Famous theorems of similar triangles Amber rubbed with fur attracts straw 2) Charging Methods 3) Measuring Charge Amber in greek: elektron Here is a narrow tomb Great Thales lies; yet his renown for wisdom reached the skies 1.b. William Gilbert ( ) 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 5 1.c. Stephen Gray ( ) [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. 6 1

2 1.d. Charles Dufay ( ) 7 1.e. Benjamin Franklin ( ) 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) 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) 2. Methods of Charging Three basic methods a) Triboelectric (friction) b) Conduction c) Induction (Influence) 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 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 10 2.a.2 Otto von Guericke a.3 Van Marum Machine (1784) 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 The biggest triboelectrostatic generator ever built, could produce voltage with any polarity. 2

3 2.a.4 Van der Graaf Generator (1929) 13 2.b. Charge by Conduction 14 If an uncharged conductor touches a charged one, the charge will be shared. When separated, they will both now have charge c.1 Charge by Induction 15 2.c.2 Charge by Induction 16 Aka charge by influence (First done by Francis Ulrich Theodore Aepinus?) Another way of doing it that is exploited by electrostatic generators 2.c.3 Electrophorus (1775) 17 2.c.4 Wimshurst Machine (1880) 18 Invented by Alessandro Volta ( ) (also invents the battery in 1800 ) Invented by James Wimshurst ( ) Two disks rotate in opposite directions, mutually inducing charge Uses method of induction to create charge 3

4 3. Measurement of Charging 19 3b Henley s Electrometer 20 Without really knowing what IS charge, how was it measured? (a) 1753 John Canton ( ) Suggests deflection angle of Pith Balls is a measure of charge First quantitative device. Deflection angle measures charge (its not however linear. Why?) 3c Electroscope 21 B. Coulomb s Law Gold Leaf Electroscope invented by Abraham Bennet ( ) 1) The Inverse Square Law 1887 Braun Electroscope is less sensitive, but more accurate 2) Coulomb s Law 3) Units of Charge B1. The Inverse Square Law 23 3a. Inverse Square Law 24 (a) Alkindus (al-kindi ), 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

5 3b. Inverse Square Law 25 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? B1b. Johannes Kepler ( ) 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 26 Sir Isaac Newton ( ) Force due to gravity = 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. GM1 M F 2 R G is the gravitational constant, measured 100 years later by Cavendish 2 27 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 only only Plus mass. 28 B2.a Joseph Priestley ( ) Friend of Franklin 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. 29 B2.b Henry Cavendish ( ) 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 little known fact that Cavendish determined that electric forces obey the inverse square law (cited by Maxwell), using charges on concentric spheres 30 5

6 B2.c Charles-Augustin de Coulomb ( ) 1785 using a torsion balance measures the inverse square law between charges. F = qq /r 2 1 dyne of force at 1 cm distance if charges are 1 statcoulomb (aka esu) 31 Coulomb's Torsion Balance This scale allows you to read the separation of the charges This dial allows you to adjust and measure the torque in the fibre and thus the force restraining the charge 32 B3. Units of Charge 33 B3a. Old Electrostatic Units Gauss shows all mechanical units can be written in terms of base units of mass, length and time Wilhelm Weber shows that all electromagnetic units can be defined by including one more base unit (for charge or current) 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 /r 2 Problem: can t relate it easily to magnetic units B3b. The Coulomb Unit 35 B3c. Permittivity of Free Space 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 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. In SI (mks) units, Coulombs law is, F = k q 1 q 2 /r 2 k=8.988x10 9 N m 2 /C 2 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. For reasons that make sense later we write k=1/4 o Permittivity of free space: o = 8.85x10-12 C 2 /N m 2 6

7 B3d. Fundamental Charge Charge is quantized 37 C. Electrodynamics Rough Draft (Notes on Board) 38 Smallest charge in nature is: e=1.67x10-19 coulombs 1) The Superposition Principle This is the charge on the proton, and negative this is the charge on the electron. 2) Force from Discrete Charges The universe appears to be electrically neutral. We don t know why its almost all matter, and hardly any antimatter. 3) Force from Continuous Charges C1. Electric Force & Newton s Laws Electrical forces cause acceleration (Newton s 2 nd law) kq 1 q 2 /r 2 =F=m 1 a 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. 39 C2. Electric Force is a VECTOR Vectors have magnitude and direction F ( F, F, F ) F iˆ F ˆj F kˆ x y z Electrical Force is a central force, the force is directed along the line between their centers, represented by vector r. qq qq F k rˆ k r 2 3 r r x y z 40 C3.a Superposition Principle & Galileo 41 C3.b Sir Isaac Newton ( ) 42 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 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. 7

8 C3.c Superposition is adding vectors Bernoulli expresses Superposition principle 1843 Möbius presents parallelogram rule for adding forces (i.e. vector-like quantities) Hamilton invents modern concept of 3D vector 1880 Gibbs invents modern system of vectors we now use 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 44 References 45 Things to Do 46 Build simple electrophorus Multimedia animations In particular, static electricity animations at Make an electroscope More on electroscopes: Leyden Jars: Finish C3 Find tesla museum stuff 8