A plane electromagnetic wave, with wavelength 3.3 m, travels in vacuum in the po

Question

A plane electromagnetic wave, with wavelength 3.3 m, travels in vacuum in the positive direction of an x axis. The electric field, of amplitude 130 V/m, oscillates parallel to the y axis. (a) What is the frequency of the wave?
  Hz

(b) What is the angular frequency of the wave?
rad/s

(c) What is the angular number of the wave?
rad/m

(d) What is the amplitude of the magnetic field component?
T
(e) Parallel to which axis does the magnetic field oscillate?

positive y positive z     negative x positive x

(f) What is the time-averaged rate of energy flow in watts per square meter associated with this wave?
W/m2

(g) If the wave falls on a perfectly absorbing sheet of area 2.2 m2, at what rate would momentum be delivered to the sheet and what is the radiation pressure exerted on the sheet?
N
Pa

Explanation / Answer

Here ,

wavelength = 3.3 m

amplitude of electric field , Eo = 130 V/m

a)

as wavelength * frequency = speed of em wave

3.3 * frequency = 3 *10^8

frequency = 9.091 *10^7 Hz

b)

angular frequency = 2 * pi * frequency

angular frequency = 2 * pi * 9.091 *10^7

angular frequency = 5.71 *10^8 rad/s

the angular frequency is 5.71 *10^8 rad/s

c)

angular number = 2pi/wavelength

angular number = 2pi/3.3

angular number = 1.904 rad/m

the angular number of the wave is 1.904 rad/m

d)

for the amplitude of magnetic field

Bo = Eo/c

Bo = 130/(3 *10^8)

Bo = 4.33 *10^-7 T

the amplitude of the magnetic field component is 4.33 *10^-7 T

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