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

§2.1 Coulomb’s law

Christopher CrawfordPHY 311

2014-02-05

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”

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Summary of mathematical theorems• Poincare

• Fundamental theorems of vector calculus

• Green’s function – inverse Laplacian

• Helmholtz theorem

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Outline• Electric charge

Properties• Electrostatic force

Coulomb’s law, why inverse square?Superposition principleUnits – 4π, ε0 vs. gravity (G)Electric field E, Displacement D

• Integration of electric fieldCharge elementExamples

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Electric charge• History, from “A Ridiculously Brief History of Electricity and Magnetism” by Ross Spencer, Brigham Young University

http://www.engr.sjsu.edu/adavis/Web02/EE140_files/history.pdf– 600 BC Thales of Miletos rubs amber (elektron in Greek) with cat fur and picks up bits of feathers. – 1500’s Girolamo Cardano elaborates the difference between amber and loadstone.– 1600 William Gilbert publishes De Magnete, coins “electric”, electric vs. magnetic effects.– 1620 Niccolo Cabeo discovers that electricity can be repulsive as well as attractive. – 1646 Thomas Browne: coins word “electricity”.– 1729 Stephen Gray shows static electricity to be transported via substances, especially metals.– 1733 Charles-Francois du Fay: vitreous (+) and resinous (-) charge; [un]like charges

[attract]repel.– 1745 Pieter van Musschenbroek invents the Leyden jar (condenser or capacitor).– 1746 William Watson suggests conservation of electric charge.– 1747 Benjamin Franklin suggests single-fluid model: + or - charge (excess or deficiency of

fluid).– 1764 Johan Carl Wilcke invents the electrophorus (induction generator)– 1766 Joseph Priestley deduces the inverse square law from hollow conducting sphere.– 1772 Henry Cavendish publishes, "An Attempt to Explain some of the Principal Phenomena of

Electricity, by Means of an Elastic Fluid.”– 1785 Coulomb independently invents the torsion balance to confirm the inverse square law

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Properties of charge• Charles François de Cisternay DuFay – 1734

1. 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.

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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

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Electric Force• Coulomb’s law

– Inverse square law: `emission’ in 4π– Central force: Newton’s 3rd 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 (α2=1/1372)

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Electric field• Action at a distance: field `carries’ force

• Displacement field: units of `charge’ instead of `force’

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Example: line charge

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Example: line charge

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Example: surface charge

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