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Electromagnetic Waves

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  1. Electromagnetic Waves Maxwell’s Equations

  2. “Sourceless” Maxwell’s Equations

  3. y E v B x A simple Electromagnetic Wave Pulse: E and B constant within a “sheet” moving at velocity v z ... need to verify consistency with Maxwell’s Equations

  4. Field lines continue forever: each field line which enters (exits) a closed surface must also enter (exit), so net number of field lines entering (exiting) a closed surface must be zero.

  5. dA dl L v dt

  6. dl L dA v dt

  7. y x a x General relations between (crossed) E and B fields creating EM waves.

  8. y x a x

  9. Classical Wave Equation!

  10. Ey Bz x Sinusoidal Electromagnetic Waves

  11. Energy in an electromagnetic wave

  12. Energy in an electromagnetic wave

  13. Energy Flow and Harmonic Waves

  14. Example: A radio station the surface of the earth emits 50 kW sinusoidal waves. Determine the intensity, and the Electric and Magnetic field amplitudes for an orbiting satellite at a distance of 100 km from the station.

  15. Momentum in an electromagnetic wave

  16. Example: Satellite in previous example has a 2m diameter antenna. What is the force of the radiation on the antenna assuming perfect reflection?

  17. Standing Waves: Superposition of equal amplitude traveling waves of opposite directions.

  18. Example: EM standing waves are set up in a cavity used for electron spin resonance studies. The cavity has two parallel conducting plates separated by 1.50 cm. • a) Calculate the longest wavelength and lowest frequency of EM standing waves between the walls. • b) Where in the cavity is the maximum magnitude electric field and magnetic field?

  19. Electromagnetic Spectrum • (see graphic) • in vacuum, v = c = 2.99792458x108 m/s • f = v increasing frequency <=> decreasing wavelength • visible spectrum: 400 nm (violet) to 700 nm (red)

  20. Q Q Radiation from a Dipole

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