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Maxwell’s equations

Maxwell’s equations. & Electromagnetic Waves . Gauss’ law for electric fields:. equivalent to Coulomb’s law. II. Gauss’ law for magnetic fields. Monopoles do not exist . Generalized Ampere's law:. The magnetic field induced around a closed path is directly related

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Maxwell’s equations

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  1. Maxwell’s equations & Electromagnetic Waves

  2. Gauss’ law for electric fields: • equivalent to Coulomb’s law

  3. II. Gauss’ law for magnetic fields Monopoles do not exist

  4. Generalized Ampere's law: The magnetic field induced around a closed path is directly related to the current inside the closed path The displacement current term is present when the current is not constant

  5. IV. Faraday’s law: • changing magnetic flux creates electric field

  6. Electromagnetic waves • Maxwell’s equations led him to realize the existence of self propagating electromagnetic waves. Using Maxwell’s equations we can see that as charges propagate they generate an electromagnetic wave which in turn induces a magnetic wave perpendicular to it.

  7. Combining ampere’s law of induction and Faraday’s law • E = electric field, B = magnetic fieldds = element of Amperian loopΦ = flux, t = timeμ0 = permeability of free spaceε0 = permittivity of free space

  8. The amplitude of the magnetic field is related to the amplitude of the electric field: Also, the two fields are everywhere orthogonal:

  9. Equating Faradays law with Ampere’s law gives This is a wave equation, with solution: E = electric field, B= magnetic field Emax= amplitude, Bmax= amplitude k= angular wave number ω= angular frequencyx = position, t= time φ= phase constant

  10. Equating Faradays law with Ampere’s law gives This is a wave equation, with solution: The propagation speed

  11. Waves traveling in a medium • Electromagnetic waves travel more slowly through a medium by a factor n: This defines n, the index of refraction.

  12. 34-2 Electromagnetic Waves The electromagnetic spectrum:

  13. Speed of light 1/((4(3.14)) -7(8.85x10-12))1/2 = 3.0x8

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