Calculating values of electric and amgnetic fields of laser beam

[krhisjun]

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 = ($$\mu$$/$$\epsilon$$)^1/2 Hoy
$$\pi$$r^2
Energy flow = 1/2 (HE + EH)
energy flow = | E x H |
E = Eo cos ($$\omega$$ 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 can't 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]

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]

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

 

[krhisjun]

Sorry, i mean to say i don't 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 I am at a loss to get any.

 

[Matterwave]

$$\bar{S}=\frac{E^2}{2\mu_0c}$$

 

[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 realize that equation,
so using those values E = $$\sqrt{2S\mu c}$$ ?
Therefore E = 119959.9933 V m^-1 ?

H = E/c$$\mu$$ ?
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 can't get that to equal but i think i may be rearranging wrong.

Thankyou for yor help so far