(a) By relation, $\frac{E_0}{B_0}$ = c Peak value of magnetic field, $B_0$ = $\frac{E_0}{c}$ = $\frac{120}{3 \times 10^8}$ = 40 × $10^{-8}$ T Angular frequency, ω = 2πu = 100π × $10^6$ Hz = π × $10^8$ Hz. Speed of light c = uλ Wavelength, λ = $\frac{c}{v}$ = $\frac{3 \times 10^8}{50 \times 10^6}$ , λ = 6 m Propagation constant, k = $\frac{2\pi}{\lambda}$ = $\frac{\pi}{3}$ rad $m^{-1}$ = 1.05 rad $m^{-1}$ (b) Let the wave is propagating along x-direction, electric field $\overset{\rightarrow}{E}$ is along y - direction and magnetic field $\overset{\rightarrow}{B}$ along z-direction. $\overset{\rightarrow}{E_y}$ = $E_0$ sin (kx - ωt) $\hat{j}$ $\overset{\rightarrow}{E_y}$ = 120 sin $\left(\frac{\pi}{3}x - \pi \times 10^8 t\right)\hat{j}$ $\hat{B}_z$ = $B_0$ sin (kx - ωt) $\hat{k}$ = 40 × $10^{-8}$ sin $\left(\frac{\pi}{3}x - \pi \times 10^8 t\right)\hat{k}$