Question

The intensity in I = (1/2?₀)E_maxB_max and in  I = E²max/(2?₀c) = (cB²_max)/(2?₀) is written in terms of the maximum electric and magnetic fields. Rewrite these equations in terms of the rms field values. (Use the following as necessary: B_rms, E_rms, c, and ?₀. Do not substitute numerical values; use variables only.)

a) I = (1/2?₀)E_maxB_max =---------------------------

b) I = E²_max/(2?₀c) =______________________

c)   I  = (cB²max)/(2?₀)=_____________________

Answer 1

Erms = Emax/sqrt 2

Emax = sqrt 2*Erms

Similarly

Bmax = sqrt 2*Brms

Part A

$I = \frac{1}{2\mu _{0}}E_{max}B_{max} = \frac{1}{2\mu _{0}}\sqrt{2}E_{rms}*\sqrt{2}B_{rms}$

$I = \frac{1}{2\mu _{0}}2E_{rms}B_{rms} = \frac{E_{rms}B_{rms}}{\mu _{0}}$

Part B

$I = \frac{E_{max}^2}{2\mu _{0}c} = \frac{(\sqrt 2E_{rms})^2}{2\mu _{0}c}$

$I = \frac{2E_{rms}^2}{2\mu _{0}c} = \frac{E_{rms}^2}{\mu _{0}c}$

Part C

$I = \frac{cB_{max}^2}{2\mu _{0}} = \frac{c(\sqrt 2E_{rms})^2}{2\mu _{0}}$

$I = \frac{2cB_{rms}^2}{2\mu _{0}} = \frac{cB_{rms}^2}{\mu _{0}}$

Please Upvote.