Answer Happy

[15] (a) Show that Maxwell's equations in free space (that is, in a region where there are no charges or currents), imply that the magnetic field obeys a three- dimensional wave equation. You may find the vector identity 7x (V A) = V(VA) - V2A helpful. (b) Show that B(x, y, z, t) = B, cos(k-r-wt) is a solution to the three-dimensional wave equation and derive an expression for the velocity of the wave in terms of electromagnetic constants. (c) Provide a sketch showing the relative phase and orientation of the electric and magnetic fields of a travelling electromagnetic wave. (d) State briefly how standing waves arise from reflections and describe the resulting phase relationship between the electric and magnetic components of an electromagnetic wave. [15] [5] [5]