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2.1 Coulombs law

• Christopher Crawford
• PHY 311
• 2014-02-05

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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 youll end
  up coming to the conclusion that theres
  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
• Greens function inverse Laplacian
• Helmholtz theorem

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Outline

• Electric chargeProperties
• Electrostatic forceCoulombs law, why inverse
  square?Superposition principleUnits 4p, e0
  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_fil
  es/history.pdf
• 600 BC Thales of Miletos rubs amber (elektron in
  Greek) with cat fur and picks up bits of
  feathers.
• 1500s 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 unlike charges
  attractrepel.
• 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
• 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.

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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

• Coulombs law
• Inverse square law emission in 4p
• Central force Newtons 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 (a21/1372)

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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