Light and Magnetic Field

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Homework Statement



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.

Homework 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

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.
 

Answers and Replies

  • #2
Simon Bridge
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Homework Helper
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I have 100 [itex]\frac{V}{m}[/itex], which isn't the irradiance [itex]E_{e}[/itex].
You are told what it is in the problem statement -
If the electric field amplitude of the wave is known to be 100V/m
... what is the relationship between the amplitude of the electric and magnetic fields?
 

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