Electric field associated with EM wave in free space is given by (...

The given electric field of the EM wave is: (E=30 \sin \left(6 $\times$10^8 t+k z\right) \hat{i}) Let's break it down: a) Direction of propagation: The term $k z$ in the equation indicates that the wave is propagating in the negative $z$ -axis (since the sign of $k z$ is positive in the sine function). Hence, the direction of propagation is along the -z axis. - b) Wavelength of the EM wave: The propagation constant $k$ is related to the wavelength by the formula (k=$\frac{2 \pi}{\lambda}$). From column-II, (k=2, $\mathrm{~m}^{-1}$), so the wavelength (\lambda=$\frac{2 \pi}{2}=\pi \approx$3.14, $\mathrm{~m}$). - c) Direction of the magnetic field: Since the electric field is along the $x$ -axis and the wave is propagating along the $z$-axis, the magnetic field must be perpendicular to both and hence lies along the -y axis. - c) Direction of the magnetic field: Since the electric field is along the $x$ -axis and the wave is propagating along the $z$-axis, the magnetic field must be perpendicular to both and hence lies along the $-y$ axis. d) Propagation constant: As discussed, the propagation constant (k=2, $\mathrm{~m}^{-1}$). Matching the columns: - a) Direction of propagation $→ s$) -z axis - b) Wavelength $→$ r) 3.14 m - c) Direction of the magnetic field $→$ p) -y axis - d) Propagation constant $→$ q) (2 $\mathrm{~m}-$1) Thus, the correct answer is: (2) a-s, b-r, c-p, d-q