Calculating values of electric and amgnetic fields of laser beam

by krhisjun
Tags: electric field, electrodynamics, magnetic field, maxwells equations
 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 = ($$\mu$$/$$\epsilon$$)^1/2 Hoy $$\pi$$r^2 Energy flow = 1/2 (HE + EH) energy flow = | E x H | E = Eo cos ($$\omega$$ 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
 P: 1,937 Since you are in vacuum, I don't think there's any reason to complicate things. E=cB, and B=μ0H
P: 22
 Quote by Matterwave 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?

P: 1,937

Calculating values of electric and amgnetic fields of laser beam

Just invert the second equation for H in terms of B.
 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.
 P: 1,937 $$\bar{S}=\frac{E^2}{2\mu_0c}$$
 P: 22 for fear of asking the obvious, S being?
 P: 1,937 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.
 P: 22 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

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