Calculating values of electric and amgnetic fields of laser beamby krhisjun Tags: electric field, electrodynamics, magnetic field, maxwells equations 

#1
Nov1910, 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 



#2
Nov1910, 01:14 PM

P: 2,080

Since you are in vacuum, I don't think there's any reason to complicate things. E=cB, and B=μ_{0}H




#3
Nov1910, 01:16 PM

P: 22





#4
Nov1910, 02:11 PM

P: 2,080

Calculating values of electric and amgnetic fields of laser beam
Just invert the second equation for H in terms of B.




#5
Nov1910, 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. 



#6
Nov1910, 04:02 PM

P: 2,080

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




#7
Nov1910, 04:20 PM

P: 22

for fear of asking the obvious, S being?




#8
Nov1910, 09:00 PM

P: 2,080

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.




#9
Nov2010, 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= 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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