A plane electromagnetic wave, with wavelength 3.18 m, travels in a free space in the direction with its electric vector , of amplitude , directed along the axis. We have to find (a) the frequency of the wave; (b) the direction and amplitude of the magnetic field associated with the wave; (c) If , the values of and ; (d) the intensity of the wave; and (e) assuming that the wave falls upon a perfectly absorbing sheet of area , the rate with which the momentum is being delivered to the sheet and the radiation pressure exerted on the sheet.
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Solution: Click For PDF Version (a)Wavelength of the plane electromagnetic wave . The frequency of the wave will be (b) The amplitude of the electric field is . As the electric and magnetic fields for a plane wave are related as , the amplitude of the magnetic field will be . As the electric field is directed along the y axis, we have . As the wave is travelling in the direction, the direction of the Pointing vector , will be . That is . From the property of the cross product we note that the magnetic field will be in the z direction. That is .
(c) We recall . Therefore, , and
(d) Intensity of the wave
(e) When the wave falls normally upon a perfectly absorbing sheet of area , the rate at which momentum will be delivered to the sheet will be
The radiation pressure exerted on the sheet will be
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