Calculating values of electric and amgnetic fields of laser beam

  • Thread starter krhisjun
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  • #1
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Homework Statement


A continuous wave laser beam in free space carries a power of 15w and has a circular cross section with diameter 1mm. Calculate peak values of the oscillatory electric and magnetic fields Eo and Ho repectively.


Homework Equations



Eox = ([tex]\mu[/tex]/[tex]\epsilon[/tex])^1/2 Hoy
[tex]\pi[/tex]r^2
Energy flow = 1/2 (HE + EH)
energy flow = | E x H |
E = Eo cos ([tex]\omega[/tex] t )


The Attempt at a Solution



Okay so i have the energy flow as 19098.593 Kj / s / m^2
I know energy flow = 1/2 \HE + EH ) = EH = |E x H| this energy flow is in direction of wave..

But i cant work out how to relate this to get the mag of electric field or magnetic field
 

Answers and Replies

  • #2
Matterwave
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Since you are in vacuum, I don't think there's any reason to complicate things. E=cB, and B=μ0H
 
  • #3
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Since you are in vacuum, I don't think there's any reason to complicate things. E=cB, and B=μ0H

Bu then HHow do i calculate H?
 
  • #4
Matterwave
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Just invert the second equation for H in terms of B.
 
  • #5
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Sorry, i mean to say i dont know how i would get H B or E.

i can see easily how with any of the variables allows the other for calculation but im at a loss to get any.
 
  • #6
Matterwave
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[tex]\bar{S}=\frac{E^2}{2\mu_0c}[/tex]
 
  • #7
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for fear of asking the obvious, S being?
 
  • #8
Matterwave
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S bar is the average of the magnitude of the Poynting Vector, it is the flux (or intensity) of the laser measured in Watts per meter squared.
 
  • #9
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Ok, didnt realise that equation,
so using those values E = [tex]\sqrt{2S\mu c}[/tex] ?
Therefore E = 119959.9933 V m^-1 ?

H = E/c[tex]\mu[/tex] ?
Therefore H = 318.4160428 A m^-1 ?

I tried to confirm the equations using dimensional analysis:
E = V m^-1
mu= kg·m·s−2·A−2
C = m S^-1
S = J s^-1 m^-2

I cant get that to equal but i think i may be rearranging wrong.

Thankyou for yor help so far
 

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