- #1

GreenPrint

- 1,196

- 0

## 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.