A sinusoidal electromagnetic wave propagates in a vacuum in the positive x-direc

Question

A sinusoidal electromagnetic wave propagates in a vacuum in the positive x-direction. The B field oscillates in the z-direction. The wavelength of the wave is 30 nm and the amplitude of the B field oscillations is 1.0×102 T.

Part A: Find the frequency with which the electric energy in the wave oscillates.

Part B: Find the frequency at which magnetic field energy oscillates.

Part C: Find the maximum energy density.

Part D: Find the minimal energy density.

Part E: Find the average energy density.

Part F: Find the intensity of the wave.

Explanation / Answer

Part A)   frequency with which the electric energy in the wave oscillates = 3 * 108/(30 * 10-9)

                                                                                                              = 1016 Hz

Part B)   frequency at which magnetic field energy oscillates =    3 * 108/(30 * 10-9)

                                                                                                   = 1016 Hz

Part C)     the maximum energy density = (8.854 * 10-12)/(2) * (1.0×102 * 3 * 108)2

                                                                           = 39.843 J/m3

Part D)    the minimal energy density = 0 J/m3

Part E)    the average energy density =     (8.854 * 10-12)/(4) * (1.0×102 * 3 * 108)2

                                                                           = 19.921 J/m3

Part F)    the intensity of the wave =    (1.0×102 * 3 * 108)2/(2 * 3 * 108 * 4 * 3.14 * 10-7)

                                                       = 1.194 * 1010 W/m2

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