§2.1 Coulomb’s law Christopher Crawford PHY

Dr. Jekyll and Mr. Hyde quote “We've all got both light and dark inside us. What matters is the part we choose to act on.” “The age-old philosophical notion of duality is readily apparent through all of Nature … These ideas date back to the dawn of mankind on this earth.” “Think about it for a while longer and you’ll end up coming to the conclusion that there’s something perpendicular in all of us” “In the same way, flux gives us an inside to the source, knowing the field lines, which are as real as Mr. Hyde.” “Although human nature has both positive and negative aspects, we are expected to express only the positive. The negative, we project into vices in order to keep them from interfering in our daily lives” 2

Summary of mathematical theorems Poincare Fundamental theorems of vector calculus Green’s function – inverse Laplacian Helmholtz theorem 3

Outline Electric charge Properties Electrostatic force Coulomb’s law, why inverse square? Superposition principle Units – 4π, ε 0 vs. gravity (G) Electric field E, Displacement D Integration of electric field Charge element Examples 4

Electric charge History, from “A Ridiculously Brief History of Electricity and Magnetism” by Ross Spencer, Brigham Young University – 600 BCThales of Miletos rubs amber (elektron in Greek) with cat fur and picks up bits of feathers. – 1500’sGirolamo Cardano elaborates the difference between amber and loadstone. – 1600William Gilbert publishes De Magnete, coins “electric”, electric vs. magnetic effects. – 1620Niccolo Cabeo discovers that electricity can be repulsive as well as attractive. – 1646Thomas Browne: coins word “electricity”. – 1729Stephen Gray shows static electricity to be transported via substances, especially metals. – 1733Charles-Francois du Fay: vitreous (+) and resinous (-) charge; [un]like charges [attract]repel. – 1745Pieter van Musschenbroek invents the Leyden jar (condenser or capacitor). – 1746William Watson suggests conservation of electric charge. – 1747Benjamin Franklin suggests single-fluid model: + or - charge (excess or deficiency of fluid). – 1764Johan Carl Wilcke invents the electrophorus (induction generator) – 1766Joseph Priestley deduces the inverse square law from hollow conducting sphere. – 1772Henry Cavendish publishes, "An Attempt to Explain some of the Principal Phenomena of Electricity, by Means of an Elastic Fluid.” – 1785Coulomb independently invents the torsion balance to confirm the inverse square law 5

Properties of charge Charles François de Cisternay DuFay – All bodies can be electrically charged by heating and rubbing, except metals and soft /liquid bodies. 2.All bodies, including metal and liquid, can be charged by influence (induction). 3.Electrical properties of an object unique to color are affected by the dye, not the color. 4.Glass is as satisfactory as silk as an insulator. 5.Thread conducts better wet than dry. 6.There are two states of electrification, Vitreous and Resinous. 7.Bodies electrified (charged) with vitreous electricity attract bodies electrified with resinous electricity and repel other bodies electrified with vitreous electricity. 6

Properties of charge +/- charge – equal and opposite – Benjamin Franklin: 1-fluid: particles / holes – Strong force has 3 pairs of +/-: red, green, blue Quantization of charge – Quarks have +2/3, -1/3 ! – Dirac showed that a magnetic monopole could explain quantization Conservation of charge – continuity equation 7

Electric Force Coulomb’s law – Inverse square law: `emission’ in 4π – Central force: Newton’s 3 rd law Units – Coulomb = 1 Amp * 1 s – Amp defined by magnetic force – Rationalized units – Electric vs. gravitational force for electron Superposition – Can add up electric field vectors due to each charge – Violated by vacuum polarization (α 2 =1/137 2 ) 8

Electric field Action at a distance: field `carries’ force Displacement field: units of `charge’ instead of `force’ 9

Example: line charge 10

Example: line charge 11

Example: surface charge 12