[UPSC CSE 2006] Electromagnetic Theory (Q391, 20M)

Starting from Maxwell's equations of electromagnetic field in vacuum obtain the classical wave equations for the four field vectors \vec{E}, \vec{D}, \vec{B} and \vec{H} . Show that the field vectors can be propagated as waves in free space with the velocity of propagation equal to 3 \times 10^8\text{ m/s}, where for free space we have the vacuum permittivity \varepsilon_o = 8.854 \times 10^{-12}\text{ farad/m} & vaccum permeability \mu_o = 1.257 \times 10^{-6}\text{ henry/m}.