$(6$ points$)$ A plane wave with a frequency of $10MHz,$ exhibiting left$-$hand elliptical

polarization, travels in the positive z$-$direction through free space. The time$-$average

Poynting vector $($representing average power density$)$ for this wave is ${10}^{-6}\frac{W}{m^2}.$

Given that the ratio of the maximum to minimum electric field intensity at any plane

$z=$ constant is $2,$ determine the maximum electric field intensity.