Max Power of 1.3cm Diameter Laser Beam Propagating Air

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The maximum electric field strength in air is 3.0 MV/m, beyond which ionization occurs, resulting in a spark. The power delivered by a 1.3 cm diameter laser beam can be calculated using the intensity formula I = P/A, where A is the area of the beam. An initial calculation using the electric field strength resulted in an intensity of 1.19 x 10^10, but an error in the radius calculation was identified. The correct radius for the 1.3 cm diameter is 0.0065 m, which affects the area used in the intensity calculation. Accurate calculations are crucial for determining the maximum power of the laser beam in air.
Linus Pauling
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1. The maximum electric field strength in air is 3.0 MV/m. Stronger electric fields ionize the air and create a spark. What is the maximum power that can be delivered by a 1.3 cm diameter laser beam propagating through air?



2. I = P/A = c*epsilon0*E2/2



3. Using E = 3*106 for E, I use the above equation to solve for I, obtaining 1.19*1010. Multiplying by area, using pi*r2 and r = 0.013m, I obtain 6.34*106, which is incorrect.
 
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the diameter is 1.3cm so the radius is only .0065m
 
****... thanks :(
 
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