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Consider a plane electromagnetic wave propagating in vacuum along the positive x

ID: 1409177 • Letter: C

Question

Consider a plane electromagnetic wave propagating in vacuum along the positive x-axis It is in vacuum, so the wave propagation speed is the speed of light c = 3 times 10^8 m/s The wave frequency is f = 85 MHz (85 times 10^6 Hz) and the maximum amplitude of the time dependent magnetic field associated with it is B_0 = 8.0 times 10^-6 T. Assume that the electric and magnetic fields E and B associated with this wave are oscillating along the y and z-axes, respectively. Calculate the following properties of this wave: a. The period T. b. The angular frequency omega. c. The wavelength lambda. d. The wavenumber k. e. The maximum amplitude E_0 of the times dependent electric field associated with it. f. The average energy density u carried weigh it. g. The average Poyntmg vector S_avg (or the average intensity I) associated with it. h. Consider a*thin sheet of solid material of area A = 300 m^2 which is placed perpendicular to the x-axis so that part of the wave hits it. Assume that there is complete reflection at the surface of the sheet. Calculate the power that this reflection produces.

Explanation / Answer

a) time ,t = 1/(85 * 106) = 1.176 * 10-8 sec

b)   angular frequency   =   2 * 3.14 * 85 * 106   = 5.338 * 108 rad/sec

c) wavelength   =   3 * 108/85 * 106   = 3.529 m

d) wave number = 2 * 3.14/3.529   =   1.779 m-1

e) maximum amplitude of electric field = 8 * 10-6 * 3 * 108 = 2400 V/m

f) average energy density = (8.854 * 10-12)/4 * (2400)2

                                                    = 1.275 * 10-5 J/m3

g) average poynting vector =   (2400 * 8 * 10-6)/(2 * 4 * 3.14 * 10-7)

                                            =    7643.31 W/m2

h)    Power reflection produces = 7643.31 * 300

                                                  =   2292993 W

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