Question

Poynting vectors S is defined as a vector whose magnitude is equal to the wave intensity and whose direction is along the direction of wave propagation. Mathematically, it is given by `S = 1/mu_0 E xx B`. Show the nature of S vs t graph.

Answer 1

Consider an electromagnetic wave. Let electric field (E) of EM wave varies along Y-axis the propagation of wave is along X-axis, then `vecE xx vecB` will give the direction of flow of energy in electromagnetic wave along X = axis.

`vecE = E_0 sin(ωt = kx)hatj`

`vecB = B_0 sin(ωt = kx)hatk`

`S = 1/mu_0 (vecE xx vecB) = 1/mu_0 sin^2 (ωt = kx)hatj xx hatk`

`S = 1/mu_0 sin^2 (ωt = kx)hati`

Variation of |S| with time will be as given in figure.