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Maxwell’s Equations

Maxwell’s Equations. & EMR. In 1864 James Maxwell developed four equations that showed that electric and magnetic fields were linked and that the fields can move through space as waves Electric field lines begin and end on electric charges. 2. Magnetic field lines are continuous.

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Maxwell’s Equations

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  1. Maxwell’s Equations & EMR

  2. In 1864 James Maxwell developed four equations that showed that electric and magnetic fields were linked and that the fields can move through space as waves • Electric field lines begin and end on electric charges

  3. 2. Magnetic field lines are continuous

  4. 3. A changing electric field will produce a magnetic field (this was difficult to detect because the magnetic fields produced by changing electric fields are very weak) • 4. A changing magnetic field will produce electric field

  5. The equations predicted the properties of the electromagnetic waves (EMR): • a.EMR is produced by accelerating electric charges, the accelerated charges lose energy, which is carried away as a wave • b. if the charges are accelerated in simple harmonic motion, the frequency of the wave = frequency of the oscillating charge SHM Animation

  6. c. the changing fields will travel through space at the speed of light (the equations predicted the speed of light) • In a vacuum: • c = 3.00 x 108 m/s • d. the magnetic field is at right angles to the electric field and both are at right angles to the direction of travel (EMR is a transverse wave) • e. light and other EMR consist of oscillating electric and magnetic fields moving together

  7. All EMR shows wave properties like reflection, refraction . . .

  8. … interference…

  9. …Polarization …

  10. … Doppler effect.

  11. The universal wave equation: where: v = speed of the wave (m/s)  = wavelength (m) f = frequency in (Hz = s-1) • Frequency vs. period where: T = period (s)

  12. Example: A radio station transmits of 144.1 MHz. Determine the wavelength and period.  = 2.08 m T = 6.94 x 10-9 s

  13. In a vacuum, all EMR travel at the speed of light regardless of frequency • 19th century physics theory said all waves had to travel through something, the medium that EMR moved was called the ether (a transparent substance that filled all space) • Experiments were done to measure the speed of light through the ether, but they all failed • All the experiments failed to locate the ether • In 1905 Einstein proposed that the ether doesn’t exist and that the speed of light is the same regardless of the speed of the source or observer

  14. EMR SPECTRUM

  15. Long wave • Wavelengths of km (low frequency) • Produced by accelerating electric currents such as AC power lines • Used in specialized communications

  16. Radio waves • metres long to hundreds of metres • produced by accelerating electrons in conductors • used in communication etc.

  17. In 1894 Hertz produced the first electromagnetic waves in a lab • He produced EMR when an induction coil created large voltages that accelerated charges across a spark gap

  18. The EMR traveled past a wire and a current was induced in the wire which sparked across a small gap • He showed that the waves traveled at the same speed as light and had all the properties of transverse waves • Radio waves are produced when electrons are accelerated back and forth along a conductor

  19. The electric field is parallel to the conductor and the magnetic field is perpendicular to the conductor • The radio wave is polarized in the direction of the conductor

  20. Microwaves • mm to cm length • produced by special vacuum tubes and circuits • used in radar, communication, heating, industry

  21. Infrared • 1 mm to the longest wavelength of visible light • produced by vibrating molecules and atoms (heat) and by special components and lasers

  22. Visible light red ~7.00 x 10-7 m (700 nm) violet ~4.00 x 10-7 m (400 nm) produced by electrons dropping from high energy levels to low energy levels

  23. Ultraviolet • less than 4.00 x 10-7 m down to 6 x 10-10 m (400 nm to 0.6 nm) • produced by electrons dropping from very high energy levels to low energy levels • used in sterilizing material, tanning, research • “ionizing radiation”, can knock electrons out of atoms and break chemical bonds

  24. X-rays • 10-8 m to 10-13 m • produced by sudden deceleration of very high speed electrons • medical and industrial imaging • “ionizing radiation”

  25. Gamma rays • 10-10 m to less than 10-14 m • produced by decelerating atomic nuclei • used in cancer treatment • ionizing radiation

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