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7.2 Maxwell Equationsthe wave equation

• Christopher Crawford
• PHY 311
• 2014-04-30

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Outline

• Review electromagnetic potential displacement
  current consequences of Faraday law and
  conservation of charge
• Physical interpretation unified symmetry in
  space and time
• Displacement current capacitor
• Electromagnetic momentum inductor
• Electromagnetic waves oscillation of energy
  between the 2
• Unification of E and B filling in the cracks
• Derivative chain different representations of
  fields
• Wave equation and solution Greens fn. and
  eigenfns

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Two separate formulations

• ELECTROSTATICS
• Coulombs law

• MAGNETOSTATICS
• Ampères law

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TWO cracks in the foundation

• Faradays law appears to violate conservation of
  energy?
• Unified gauge transformation for V and A
• Continuity equation vs. Ampères law

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Example current through a capacitor

• Which surface should oneuse for Ampères law?

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Example 7.8 potential momentum

• Angular momentum from turning off the field
• Potential momentum associated with the field
• Magnetic field energy acts as electromagnetic
  inertia

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Magnetic field energy

• Work against the back-EMF is stored in the
  magnetic field
• It acts as electrical inertia to keep current
  moving

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Electromagnetic Waves

• Sloshing back and forth between electric and
  magnetic energy
• Interplay Faradays EMF ? Maxwells
  displacement current
• Displacement current (like a spring) converts E
  into B
• EMF induction (like a mass) converts B into E
• Two material constants ? two wave properties

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One unified formulation

• ELECTROMAGNETISM

• Faradays law stitches the two formulations
  togetherin space and time
• Previous hint continuity equation

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Unification of E and B

• Projections of electromagnetic field in space and
  time
• That is the reason for the twisted symmetry in
  field equations

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Unification of D and H

• Summary