Calculating values of electric and amgnetic fields of laser beam

krhisjun

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

Matterwave

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

krhisjun

Bu then HHow do i calculate H?

Matterwave

Just invert the second equation for H in terms of B.

krhisjun

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

[tex]\bar{S}=\frac{E^2}{2\mu_0c}[/tex]

krhisjun

for fear of asking the obvious, S being?

Matterwave

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

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