b
\(E_{y}=2.5 \frac{\mathrm{N}}{\mathrm{C}}\left[\left(2 \pi \times 10^{6} \frac{\mathrm{rad}}{\mathrm{m}}\right) t-\left(\pi \times 10^{-2} \frac{\mathrm{rad}}{\mathrm{s}}\right) x\right]\)

\(E_{z}=0\)

The wave is moving in the positive direction of \(x .\)

This is the form \(E_{y}=E_{0}(\omega t-k x)\)

\(\omega= 2 \pi \times 10^{6} \)

\(2 \pi v= 2 \pi \times 10^{6} \Rightarrow \mathrm{v}=10^{6}\, \mathrm{Hz} \)

\(\frac{2 \pi}{\lambda}=k \Rightarrow  \frac{2 \pi}{\lambda}=\pi \times 10^{-2} \)

\(\Rightarrow \lambda=\frac{2 \pi}{\pi \times 10^{-2}} =2 \times 10^{2}=200\, \mathrm{m}\)