Answer
a) y direction
b) $\lambda=0.149mm$
c) $\vec{B}(y,t)=(1.03\times10^{-3}T)\hat{i}\cos((4.22\times10^{4}rad/m)y-(12.65\times10^{12}rad/s)t)$
Work Step by Step
a) The electric field is propagating in the z direction and the electromagnetic wave is moving in the y direction.
b) $f=\frac{12.65\times10^{12}rad/s}{2\pi}=2.01\times10^{12}Hz$. The wavelength is given by $\frac{v}{f}=\frac{3.0\times10^8m/s}{2.01\times10^{12}Hz}=0.149mm$
c) $B_0=\frac{E_0}{c}=\frac{3.10\times10^5V/m}{3.0\times10^8m/s}=1.03\times10^{-3}T$
The magnetic field will propagate in the x direction.
The coefficient of y is $\frac{2\pi}{\lambda}=\frac{2\pi}{0.149mm}=4.22\times10^{4}rad/m$.
$\vec{B}(y,t)=(1.03\times10^{-3}T)\hat{i}\cos((4.22\times10^{4}rad/m)y-(12.65\times10^{12}rad/s)t)$
