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Light and Magnetic Field

  1. Sep 2, 2013 #1
    1. The problem statement, all variables and given/known data

    I'm not sure if this goes in introductory physics for not, but anyways...

    A light wave is traveling in glass of index 1.50. If the electric field amplitude of the wave is known to be 100 [itex]\frac{V}{m}[/itex], find (a) the amplitude of the magnetic field and (b) the average magnitude of the Poynting vector.

    2. Relevant equations


    [itex]E_{e} = \frac{power}{area}[/itex]
    [itex]E_{e} = \frac{1}{2}ε_{0}cE_{0}^{2}[/itex]
    [itex]n = \frac{c}{\upsilon}[/itex]
    [itex]E_{0} = cB_{0}[/itex]
    [itex]S = ε_{0}c^{2}E_{0}B_{0}[/itex]
    [itex]P = IV[/itex]

    Where
    [itex]E_{e}[/itex] is the irradiance
    [itex]c ≈ 2.998 X 10^{8} \frac{m}{s}[/itex] is the speed of light
    [itex]E_{0}[/itex] is the magnitude of the magnetic field
    [itex]ε_{0} ≈ 8.8542 X 10^{-12} \frac{(C s)^{2}}{kg m^{3}}[/itex] is the permittivity of vacuum
    n is the refractive index of a material
    [itex]\upsilon[/itex] is the velocity of light through the material
    [itex]B_{0}[/itex] is the magnitude of the magnetic field
    S is the magnitude of the Poynting vector
    P is power
    V is voltage
    I is current

    3. The attempt at a solution
    For part (a)
    I seem to be having some issues processing the given information. I know that irradiance [itex]E_{e}[/itex] is power [itex]P[/itex] divided by area[itex]A[/itex]. I have 100 [itex]\frac{V}{m}[/itex], which isn't the irradiance [itex]E_{e}[/itex]. Without being able to find the irradiance [itex]E_{e}[/itex] I'm not sure how to proceed. I'm unsure how to apply the knowledge of the refraction index n. I can solve for the speed of the light through the material [itex]\upsilon[/itex] but I'm not sure what good that really does.

    [itex]n = \frac{c}{\upsilon}[/itex]
    [itex]\upsilon = \frac{c}{n} = \frac{2.998 X 10^{8} \frac{m}{s}}{1.5} ≈ 1.999 X 10^{8} \frac{m}{s}[/itex]

    Once I find the irradiance I can solve for amplitude of the electric field
    [itex]E_{e} = \frac{1}{2}ε_{0}cE_{0}^{2}[/itex]
    [itex]E_{0} = \sqrt{\frac{2E_{e}}{ε_{0}c}} = \sqrt{\frac{2E_{e}}{(2.998 X 10^{8} \frac{m}{s})(8.8542 X 10^{-12} \frac{(C s)^{2}}{kg m^{3}})}}[/itex]

    Once I get this value I can solve for the amplitude of the magnetic field
    [itex]E_{0} = cB_{0}[/itex]
    [itex]B_{0} = \frac{E_{0}}{c}[/itex]

    For part (b)
    Once I solve part A I can solve for the average magnitude of the Poynting vector rather easily

    [itex]S = ε_{0}c^{2}E_{0}B_{0} = (8.8542 X 10^{-12} \frac{(C s)^2}{kg m^{3}})(2.998 X 10^{8} \frac{m}{s})E_{0}B_{0}[/itex]

    Thanks for any help that anyone can provide me in solving this problem.
     
  2. jcsd
  3. Sep 2, 2013 #2

    Simon Bridge

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    You are told what it is in the problem statement -
    ... what is the relationship between the amplitude of the electric and magnetic fields?
     
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