A plane electromagnetic wave with wavelength 5.0 m and polarizationin the z-dire

Question

A plane electromagnetic wave with wavelength 5.0 m and polarizationin the z-direction travels in a
vacuum in the positive y-direction, with an electric field E ofmaximum amplitude 200 V/m. (a) What is the frequency of the wave,in Hz? (b) What is the maximum amplitude, as well as the direction,of the
magnetic field B corresponding to this wave? (c) What is thetime-averaged energy flow associated with
this wave, expressed in W/m2? (d) If the wave falls on a perfectlyabsorbing surface of area 2.0 m2, lying
in the x&z plane, what is the net force on this surface that isproduced by the wave?

Explanation / Answer

The frequency of the wave is     f = V /       = 3x108 m/s /5       = 60x106 Hz       = 60MHz The amplitude of the magnetic field is      B = E /c         = 200 /3x108         =6.67x10-7 T The time average energy flow is given as      S= E2 / 2o c        = (200)^2 /2(4x10-7)(3x108)               = 53.1W/m^2   radiation pressure P = S / c as P = F /A    Force    F = SA / c      = ( 53.1 W/m^2 )(2)/(3x108 m/s )     = 3.536x10-7 N

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