Unification of Electricity and Magnetism

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Unification of Electricity and Magnetism

• Maxwells theory combining Faradays law and
  Amperes law

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Unifications

• There have been several important Unifications in
  Physics
• Unification of Electricities
• Unification of Electricity and Magnetism
• Special Relativity
• Unification of EM and Quantum Mechanics
• Unification of EM and Weak Force
• Yet to come
• Unification of Gravity and Quantum Mechanics

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What is so Special about Unification?

• Is it nothing more than being able to write down
  a theory in one equation instead of two?
• Each Unification brought with it a surprise, a
  new understanding, and new phenomenon
• Putting the pieces of a puzzle together revealed
  missing pieces

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Unification of Electricity and Magnetism

• James Clerk Maxwell combined
• Faradays law describing how electric field is
  made from magnetic field
• Amperes law describing how magnetic field is
  made from current
• Gauss law describing how electric field is made
  from charge
• into a single set of equations

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Michael Faraday September 1821
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Electric Field

• The force between charge is given by Coulombs
  law

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Electric Field
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Electric and Magnetic Fields
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Electric Fields from Magnets

• When a current flows through a wire a magnetic
  field circles the wire
• If currents can make magnetic fields, can magnets
  make electric fields?
• When a magnet is moving through a coil a voltage
  is induced at the ends of the coil
• This is known as Faraday Inductionand is the key
  principle for the operation of all motors and
  generators

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Magneto-Electricity

• The magnetic field moving through the coil can be
  either
• A magnet that inserted into the coil
• A magnetic field produced by a current in, for
  example, another coil
• Faraday Induction

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Early Generator

• Two sets of coils
• One with a current to make a magnetic field
• The second had a voltage induced
• Device was based on steam engine technology

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James Clerk Maxwell

• Born 1831
• Color Vision, 1850
• Saturns Rings, 1855
• Statistical and Molecular Physics, 1859
• A dynamical Theory of the Electric Field, 1864

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Amperes Law
The magnetic field around a loop is proportional
to the current going through the loop
Magnetic Field inside a Solenoid
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Maxwells Addition
Maxwell added another term to Amperes Law one
that had not been observed
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Faraday Induction

• Maxwell did not have the advantage of vector
  notation. In describing the magnetic field he
  used three functions, F, G, H, for the components
  of the field.

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Speed of Light

• After 85 pages of derivations, Maxwell was able
  to find the equation for an electro-magnetic
  wave.
• The velocity of the wave was close to the speed
  of light

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Unification of Electricity and Magnetism

• The connection Faradays Law connected Electric
  Field to Magnetic Field
• The Unified Theory Maxwell, by adding
  displacement current, came up with the single
  theory describing electricity and magnetism
• The surprise - Light is an electromagnetic wave
• Further examination of the theory lead to the
  predictions of Special Relativity

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Conclusion

• This is the first of the theoretical unifications
• Unifications are foreshadowed by a connection
  in this case the electric and magnetic field
• We will see similar connections next time when we
  look at
• unification of EM with Quantum Mechanics
• unification of Special Relativity with Quantum
  Mechanics
• unification of the Electric and Weak forces
• unification of Gravity and Quantum Mechanics