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5.1 Magnetic Field

• Christopher Crawford
• PHY 417
• 2015-01-16

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Outline

• Magnetic field and torque
• William Gilbert field lines of permanent
  magnets Hans Christian Ørsted magnetic field
  of a current
• Magnetostatics
• André-Marie Ampère force on two straight wires
• Current element continuity equation

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Static force laws

• Electrostatics Coulombs law

• Magnetostatics Biot-Savart law

B.C.s Flux lines bounded by charge Flux lines
continuous Flow sheets continuous
(equipotentials) Flow sheets bounded by current
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History of magnetism

• The magnetic force was known in antiquity
• Magnetism more predominant in nature but more
  difficult to quantify
• Permanent magnets (magnetization), not electric
  currents
• No magnetic (point) charge (monopole) gt dipole
  effect (N,S poles)
• 1-d currents instead of 0-d charges gt cant
  split a wire!
• Static electricity produced in the lab long
  before steady currents
• Timeline (from A Ridiculous Brief History of
  Electricity and Magnetism)
• 600 BC Thales of Miletus discovers lodestones
  attraction to iron
• 1200 AD Chinese use lodestone compass for
  navigation
• 1259 AD Petrus Peregrinus (Italy) discovers the
  same thing
• 1600 AD William Gilbert discovers that the Earth
  is a giant magnet
• 1742 AD Thomas LeSeur shows inverse cube law for
  magnets
• 1820 AD Hans Christian Ørsted discovers that
  current twists magnets Andre Marie Ampere shows
  that parallel currents attract/repel
  Jean-Baptiste Biot Felix Savart show inverse
  square law

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Early magnetism

• https//www.tcd.ie/Physics/Magnetism/Guide/compass
  .php
• Wu Ching Tsung Yao (1040)
• First mention of the magnetic compass
• Petrus Perigrinus (1269)
• Epostolia de Magnete rediscovered it
• William Gilbert (1600)
• De Magnete the earth is a magnet
• René Descartes
• effluvia of "threaded parts

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Magnetic fields

• In magnetism it is more natural to start with the
  concept of Magnetic field than the actual force
  law! (dipole)
• Compass alignswith B-field
• Iron filings lineup along magneticfield lines

• Magnetic field lines look like an electric dipole
  (in fact the magnetic dipole was discovered
  first!)

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Iron Filings
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Iron Filings
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Difference between E, B dipoles

• Same as the differences between Flux and Flow!

• Charge sources of flux
• Conservative flow potential
• Example Amber (electric)
• Rub to charge
• 2 charges (/) monopole fluids
• Exerts force on charges

• Continuous field lines flux
• Rotational (source of flow?)
• Example Lodestone (magnet)
• Always charged
• 2 poles (N/S) inseparable dipole
• Exerts torque on other magnets

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First connection to currents

• from Wittaker, A history of the theories of
  Aether and Electricity

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The current connection

• There is no magnetic monopole N/S cannot be
  separated
• The source of all magnetism is electric current
• A dipole is just a current loop
• Hans Christian Ørsted
• Current produces B-field
• Quantified by Biot Savart

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Hans Christian Ørsted

• from Wittaker, A history of the theories of
  Aether and Electricity

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Electrodynamics

• André-Marie Ampère showed that parallel currents
  attractand antiparallel currents repel
• The magnetic force is the basis for
  electromagnetic units

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Ampères generalization

• Experimental laws
• Force formula
• Problem
• The force between two current elements does
  NOTpoint along the line from the one to the
  other!

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Peer criticism
MAXWELL
HEAVISIDE
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Current elements

• Analogous to charge elements different
  dimensions
• Relations between charge / current and different
  dimensions analogy multi-lane highway
  current flux

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Continuity equation

• Local conservation of charge
• Current I is a flux current density J
  flux density
• 4-vector current