# Calculating values of electric and amgnetic fields of laser beam

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

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

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

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

for fear of asking the obvious, S being?

Matterwave
Gold Member
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.

Ok, didnt realise 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 cant get that to equal but i think i may be rearranging wrong.

Thankyou for yor help so far