Answer
(a) $\frac{1}{\sqrt{\epsilon_{\circ}\mu_{\circ}}}$
(b) $3.00\times 10^8m/s$
Work Step by Step
(a) We can find the required ratio as follows:
$\frac{E^2}{B^2}=\frac{2}{2\epsilon_{\circ}\mu_{\circ}}$
$\implies \frac{E^2}{B^2}=\frac{1}{\epsilon_{\circ}\mu_{\circ}}$
$\implies \frac{E}{B}=\frac{1}{\sqrt{\epsilon_{\circ}\mu_{\circ}}}$
(b) We know that
$\frac{E}{B}=\frac{1}{\sqrt{\epsilon_{\circ}\mu_{\circ}}}$
We plug in the known values to obtain:
$\frac{E}{B}=\frac{1}{\sqrt{(8.85\times 10^{-12})(4\pi \times 10^{-7})}}$
$\frac{E}{B}=3.00\times 10^8m/s=c$
