Question

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 1.5cm diameter laser beam propagating through air?

Answer 1

Answer:

The value is  $P_{max} = 2.11 * 10^{6} \ W$

Explanation:

From the question we are told that  

    The maximized electric field strength is  $E = 3.0 \ MV/m = 3.0 *10^{6} \ V/m$

     The diameter is  $d = 1.5\ cm = 0.015 \ m$

Generally the cross -sectional area is mathematically represented as

 =>      $A = \frac{\pi * d^2 }{4}$

 =>      $A = \frac{3.142 * 0.015^2 }{4}$

 =>      $A = 0.0001767 \ m^2$

Generally the maximum power is mathematically represented as

       $P_{max} = \frac{E_{max}^2}{ 2 * \mu_o * c } * A$

Here c is the speed of light with value  $c = 3.0 *10^{8} \ m/s$

        $\mu_o$ is the permeability of free space with value  $\mu_o = 4 \pi *10^{-7} \ H/m$

      $P_{max} = \frac{ (3.0 *10^{6})^2}{ 2 * (4 \pi *10^{-7}) * 3.0 *10^{8} } * 0.0001767$

=>   $P_{max} = 2.11 * 10^{6} \ W$