The given electric field is $E_{x} = E_{0} \sin(kz - \omega t)$. Comparing this with the given equation $E_{x} = E_{0} \sin(kz - 2\pi \times 10^{6}t)$, we identify the angular frequency $\omega = 2\pi \times 10^{6} \text{ rad/s}$. The negative sign between $kz$ and $\omega t$ indicates propagation in the $+z$ direction. Thus, option (A) is correct.
The speed of an electromagnetic wave in a medium is given by $v = \frac{c}{\sqrt{\epsilon_{r}}}$. Given $\epsilon_{r} = 9$ and $c = 3 \times 10^{8} \text{ m/s}$, we have: $$v = \frac{3 \times 10^{8}}{\sqrt{9}} = \frac{3 \times 10^{8}}{3} = 10^{8} \text{ m/s}$$ Thus, option (B) is correct.
The wavelength $\lambda$ is given by $\lambda = \frac{v}{f}$. Since $\omega = 2\pi f$, we have $f = \frac{\omega}{2\pi} = \frac{2\pi \times 10^{6}}{2\pi} = 10^{6} \text{ Hz}$. $$\lambda = \frac{10^{8}}{10^{6}} = 100 \text{ m}$$ Option (C) states the wavelength is 300 m, which is incorrect.
The relationship between electric and magnetic field amplitudes is $E_{0} = v B_{0}$, or $B_{0} = \frac{E_{0}}{v}$. The magnetic field is $B_{y} = \frac{E_{0}}{v} \sin(kz - \omega t)$. Option (D) suggests $B_{y} = \frac{B_{0}}{v} \sin(...)$, which is dimensionally inconsistent and incorrect in form. However, in the context of identifying the "incorrect" choice, (C) is mathematically false based on the calculation.
Final Answer: C
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