Chapter 22, Problem 35P

To determine

The rms electric field strength of the beam.

Answer to Problem 35P

The answer is $1.459V/m$ .

Explanation of Solution

Given info:

Power, $L=10kW=1.0\times {10}^{4}W$

Permittivity of free space, ${\epsilon }_0=8.85\times {10}^{-12}{C}^2/N\cdot m^2$

Radius, $r=750m$

Formula used:

Formula to calculate the rms electric field strength:

  $E_{rms}=\sqrt{\frac{P}{Ac{\epsilon }_0}}=\sqrt{\frac{P}{\pi r^{2}c{\epsilon }_0}}$

Where,

  $P$ is power, $A$ is area, $c$ is factor which is equals to $3.0\times {10}^{8}m/s$ , $r$ is a radius, ${\epsilon }_0$ is permittivity of free space, $\pi$ is constant.

Calculation:

Substitute all the given and known values in formula: $E_{rms}=\sqrt{\frac{P}{\pi r^{2}c{\epsilon }_0}}$

  $E_{rms}=\sqrt{\frac{1.0\times {10}^{4}W}{\pi {\left(750\right)}^2\left(3\times {10}^8\right)\left(8.85\times {10}^{-12}{C}^2/N\cdot m^2\right)}}=1.459V/m$

Conclusion: The required rms electric field is $1.459V/m$ .