For a plane y-polarized wave with intensity E 0 and wavelength 2 m is propagatin

Question

For a plane y-polarized wave with intensity E0 and wavelength 2 m is propagating in the x-z plane, incident at 30 deg. from normal from free space on a perfect electric conductor with an infinite planar boundary at z = 0, what is:

a) The wavenumber direction k^ in free space?

b) The transverse component kx and the normal component kz on both sides of the boundary (free space / PEC)?

c) A reflected wave is generated to satisfy the boundary conditions at z = 0. What is the wavenumber direction of this reflected wave? What is its amplitude? Show that the transverse boundary condition on Ey is satisfied.

d) Find the corresponding magnetic field phasor for the incident and reflected waves, indicating the amplitude, polarization vector components, and phase dependence.

e) Use the transverse boundary condition on magnetic field to find the surface current.

f) Find the time domain representation of the total electric field.

Explanation / Answer

(A) Wave number (K)=2*pi/Wavelength=2*3.14/2=3.14/meter.

(B). The incoming angle is of 30o. So, Kx=K. cos (30o)=K.(0.866)=2.72/meter

   Kz=K. Sin(30)=1.57/meter and sum of these two vectors will give total K.

(C) Since wavelength is a fundamental property, wavelength of the reflected wave will be same and hence wave number will be same.

(D). Since the wave is propagating in the Z direction and electric field is present in the Y direction, there is only one diretion for the magnetic field to be present and that direction is X direction because electromagnetic wave is of transverse electromagnetic by nature.

N=Intrinsic Impedance of free space.

According to the definition, amplitude of the magnetic field Ho=Eo/N

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