A commerically available hand-held green laser has a power of 4.4W and produces

Question

A commerically available hand-held green laser has a power of 4.4W and produces a beam of radius 0.44mm. The laser will cut through plastic and set wood on fire, so it makes a great Christmas present. What is the amplitude of the electric field in the beam? If manned space missions to the planet Mercury are ever planned, those missions will have to deal with the intensity of the solar radiation at Mercury. The energy output of the sun is 3.846 Times 10^26 W. The radius of Mercury's orbit is 58 Times 10^9 m. Calculate the intensity of sunlight at Mercury's surface.

Explanation / Answer

14.1)

power per unit area = P/A = 0.5*[1/(c*mu_o)]*Em^2

c i sthe speed of light = 3*1068 m/s

mu_o = permeability of free space = 4*pi*10^-7 H/m

Em is the req   uired amplitude of electric field

4.4/(3.142*0.44*0.44*10^-6) = 0.5*[1/(3*10^8*4*3.142*10^-7)]*Em^2

7.23*10^6 = 0.01326*10^-1*Em^2

Em = 73.84*10^3 = 7.4*10^4 N/C

then the answer is 7.4*1064 N/C

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14.2) intensity I = power /surface area = P/(4*pi*R^2) = 3.846*10^26/(4*3.142*58*58*10^18) = 9.0967*10^-5*10^8 = 9096.7 = 9100 W/m^2

So the aNSWER IS b) 9100 W/m^2

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