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Calculating values of electric and amgnetic fields of laser beam

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krhisjun
#1
Nov19-10, 11:39 AM
P: 22
1. The problem statement, all variables and given/known data
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.


2. Relevant 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 )


3. 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
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Matterwave
#2
Nov19-10, 01:14 PM
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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
krhisjun
#3
Nov19-10, 01:16 PM
P: 22
Quote Quote by Matterwave View Post
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?

Matterwave
#4
Nov19-10, 02:11 PM
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Calculating values of electric and amgnetic fields of laser beam

Just invert the second equation for H in terms of B.
krhisjun
#5
Nov19-10, 02:48 PM
P: 22
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.
Matterwave
#6
Nov19-10, 04:02 PM
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[tex]\bar{S}=\frac{E^2}{2\mu_0c}[/tex]
krhisjun
#7
Nov19-10, 04:20 PM
P: 22
for fear of asking the obvious, S being?
Matterwave
#8
Nov19-10, 09:00 PM
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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.
krhisjun
#9
Nov20-10, 08:23 AM
P: 22
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= kgms−2A−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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