An electromagnetic wave in a vacuum traveling in the +x direction generated by a
ID: 582503 • Letter: A
Question
An electromagnetic wave in a vacuum traveling in the +x direction generated by a variable source initially has a wavelength of 205 m and a maximum electric field Emax in the +y direction of 3.80×103 V/m . If the period of the wave is then increased by a factor of 2.70, what is the equation of the resulting magnetic field component of the wave?
What are the coefficients in the equation for the magnetic field component of the wave after the period increases by a factor of 2.70?
B=Bocos(kx-wt) <---- what is Bo, k and w(omega)?
Explanation / Answer
An electromagnetic wave is a traveling wave perpendicular, this means that the electric and magnetic fields oscillate in directions perpendicular to the direction of travel of the wave
E = Eo Cos (k x – w t )
B = Bo Cos (k x – wt )
in the exercise they say E ranges in the +y direction, in concernencia the only direction left is B ranges in the + z
w is the angular velocity of the wave, it is related to frequency using expressions rotational kinematics
w = 2 f f = 1/ T
where
f It is the frequency
T It is the period
w = 2 /T
the given condition is
T = 2.70 To
w = 2/ 2.70 To w = 1/2.70 2/To
w = 0.37 wo
we substitute in equation E y B
Ey = Eo Cos (k x – 0.37 wo t )
Bz = Bo Cos (k x – 0.37 wot )
It is noted that the change is that the frequency of the wave decreases
calculate the vaules of the parameter
k It is the wavevector
k = 2/
k = 2/ 205 10-6
k = 3.065 104 m-1
calculate wo
wo/k = c wo = c k
wo = 3 108 3.065 104
wo = 9.195 1012 s-1
Eo = Emax = 3.80 10-3 V/m
calculate Bo with the equation
Eo/Bo = c
Bo = Eo/c
Bo = 3.80 10-3/ 3 108= 1.26 10-11T
Now we substitute these values in expressions
Ey = 3.80 10-3 Cos (3.065 104 x – 0.37 9.195 1012 t )
Bz = 1.26 10-11Cos (3.065 104x – 0.37 9.195 1012t )
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