A continous-wave (cw) argon-ion laser beam has an average power of 53W and a bea

Question

A continous-wave (cw) argon-ion laser beam has an average power of 53W and a beam diameter of 6mm. Assume that the intensity of the beam is the same throughout the cross section of the beam ( a real beam has an intensity distribution that is a Gaussian function).

A. Calculate the intensity of the laser beam. Answer given is 1.87*10^6 W/m^2

B. Compare this with the average intensity of sunlight at Earth's surface (1400 W/m^2). Answer given is 1340

C. Find the ( magnitude of the ) root-mean-square electric field in the laser beam. Answer given is 26600V/m

D. Calculate the (magnitude of the) root-mean-square value of the magnitude field in the laser beam. Answer given is 8.86*10^-5T

Explanation / Answer

A. apply here the formula for intensity I = Power/area = Erms^2/uoC

where
Area A = pi r^2

r = d/2   = 6/2 = 3 mm

Erms = eelctric field

uo is constant = 4pi e-7

and C is velocity of light   = 3e8 m/s

so

part A : I = 53/(3.14* 3e-3*3e-3)

I = 1.87 *10^6 W/m^2 ------<<<<<<<<answer to part A

--------------------------------------
part B:

ratio of I/Io = 1.87 e6/1400

ratio   = 1340 ------<<<<<<<<answer to part B

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C.

Erms^2 = I * uoC

Erms^2 = 1.87 e6 *4*3.14e-7 * 3e8

Erms^2 =    7.046 *10^8

ERrms = 26544 N/C or 26600 N/C ------<<<<<<<<answer to part C

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D. Erms   = Brms * c

so Brms =   26600/3e8

Brms = 8.85 *10^-6 Tesla ------<<<<<<<<answer to part D

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