Question

Electromagnetic waves transport energy. This problem shows you which parts of the energy are stored in the electric and magnetic fields, respectively, and also makes a useful connection between the energy density of a plane electromagnetic wave and the Poynting vector. In this problem, we explore the properties of a plane electromagnetic wave traveling at the speed of light c along the x axis through vacuum. Its electric and magnetic field vectors are as follows: E = E, sin (kx – wt) j, B= B0 sin (kx – wt)k. Throughout, use these variables ( E, B, E9, Bo, k, x, and w) in your answers. You will also need the permittivity of free space eo and the permeability of free space uo. Note: To indicate the square of a trigonometric function in your answer, use the notation sin(x)^2 NOT sin^2(x).

Answer 1

Porta Ug(t) = 12 & ² = 1 Es to sin (Kx - cost)? = { E. E(sin(kx-604) Part B Upd) = ente = (Be sin(kxcot)]" = Lite (sinke-est)** Parte The average of square of sine function is f it son average value of (sin(kx-wt) ² = £ in Uge = 1 E Ext Part E Part D up = Ba xz = Part E U = UE + UB A E o Bo= Eo Follo o u = 466+ io e ten 465* + 4 u = LEED Part E z a Ē x B - Eo sin(kx-cat) Î x Bosin(kx-wf]k Mo مل

Mo = E. Bo (sin(kx-cos)? Ĉ (* = 1) now - bc (speed of his Emwane) =) Bo= Eola :3 = (sin(kx-04)? Time: Averaged Poynting reader (3) - E xt ? Clo (3) = {cat în