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Maxwell’s Equations in Free Space with no free charges or currents:

Discover the fundamental principles of electromagnetic waves and Maxwell's equations in free space with no free charges or currents. Learn about Gauss, Faraday, Ampere-Maxwell equations, vector Laplacian, wave equations for B and E fields, permittivity and permeability of free space, traveling and standing waves, and the phase relationship in Faraday's Law.

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Maxwell’s Equations in Free Space with no free charges or currents:

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  1. Electromagnetic Waves Maxwell’s Equations in Free Space with no free charges or currents: Gauss No Monopoles Faraday Ampere-Maxwell Take the time derivative of Faraday:

  2. Substitute in Ampere-Maxwell

  3. 1st derivatives 2nd derivatives Function: Field:

  4. “Vector Laplacian”

  5. Substitute in Ampere-Maxwell 0 3D Wave equation for B

  6. Similar derivation for the E field: 3D Wave equation for E e0 = permittivity of free space = 8.85 x 10-12 C/Nm2 m0 = permeability of free space = 4p x 10-7 N/A2

  7. Stretched String: Traveling Waves Standing Waves Simple Guess: traveling wave with E field along x, moving along z: Wave Equation now:

  8. What about B? Faraday’s Law: Note: are in phase

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