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574.


Problem 41.39 (RHK)


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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(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