2 1 Coulombs law Christopher Crawford PHY 311

§ 2. 1 Coulomb’s law Christopher Crawford PHY 311 2014 -02 -05

Summary of mathematical theorems • Poincare • Fundamental theorems of vector calculus • Green’s function – inverse Laplacian • Helmholtz theorem 2

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 3

Electric charge • History – – – – 600 BC 1500’s 1600 1620 1646 1729 1733 1745 1746 1747 1764 1766 1772 – 1785 Thales of Miletos rubs amber (elektron in Greek) with cat fur and picks up bits of feathers. Girolamo Cardano elaborates the difference between amber and loadstone. William Gilbert publishes De Magnete, coins “electric”, electric vs. magnetic effects. Niccolo Cabeo discovers that electricity can be repulsive as well as attractive. Thomas Browne: coins word “electricity”. Stephen Gray shows static electricity to be transported via substances, especially metals. Charles-Francois du Fay: vitreous (+) and resinous (-) charge; [un]like charges [attract]repel. Pieter van Musschenbroek invents the Leyden jar (condenser or capacitor). William Watson suggests conservation of electric charge. Benjamin Franklin suggests single-fluid model: + or - charge (excess or deficiency of fluid). Johan Carl Wilcke invents the electrophorus (induction generator) Joseph Priestley deduces the inverse square law from hollow conducting sphere. Henry Cavendish publishes, "An Attempt to Explain some of the Principal Phenomena of Electricity, by Means of an Elastic Fluid. ” Coulomb independently invents the torsion balance to confirm the inverse square law 4

Properties of charge • Charles François de Cisternay Du. Fay – 1734 1. 2. 3. 4. 5. 6. 7. All bodies can be electrically charged by heating and rubbing, except metals and soft /liquid bodies. All bodies, including metal and liquid, can be charged by influence (induction). Electrical properties of an object unique to color are affected by the dye, not the color. Glass is as satisfactory as silk as an insulator. Thread conducts better wet than dry. There are two states of electrification, Vitreous and Resinous. Bodies electrified (charged) with vitreous electricity attract bodies electrified with resinous electricity and repel other bodies electrified with vitreous electricity. 5

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 6

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=1/1372) 7

Electric field • Action at a distance: field `carries’ force • Displacement field: units of `charge’ instead of `force’ 8

Example: line charge 9

Example: surface charge 10

Example: surface charge 11