Answer
(a) The average energy density is $4.67\times 10^{-6}~J/m^3$
(b) $E_{rms} = 726~V/m$
$B_{rms} = 2.42\times 10^{-6}~T$
Work Step by Step
(a) We can find the average energy density:
$\frac{I}{c} = \frac{1400~W/m^2}{3.0\times 10^8~m/s} = 4.67\times 10^{-6}~J/m^3$
The average energy density is $4.67\times 10^{-6}~J/m^3$
(b) We can find $E_{rms}$:
$E_{rms}^2 = \frac{I}{c~\epsilon_0}$
$E_{rms} = \sqrt{\frac{I}{c~\epsilon_0}}$
$E_{rms} = \sqrt{\frac{1400~W/m^2}{(3.0\times 10^8~m/s)~(8.85\times 10^{-12}~C^2/N~m^2)}}$
$E_{rms} = 726~V/m$
We can find $B_{rms}$:
$B_{rms} = \frac{E_{rms}}{c}$
$B_{rms} = \frac{726~V/m}{3.0\times 10^8~m/s}$
$B_{rms} = 2.42\times 10^{-6}~T$
