If the electric field intensity traveling wave, polarized in the x-direction. is

Question

If the electric field intensity traveling wave, polarized in the x-direction. is described by and it is known that it is a TEM wave traveling in a lossless dielectric medium with intrinsic impedance n = 0. 01 [ ohm ] Determine: The wave speed The wavelength The frequency The amplitude of the electric field intensity wave The direction of the magnetic field intensity wave The magnitude of the magnetic field intensity wave The relative permittivity of the medium The relative permeability of the medium

Explanation / Answer

general wave equation:
e(z,t) = e0 cos(wt-kx)..............(1)

w: frequency of the wave in rad/s

k: propagation constant

1) wave speed: v= coefficient of "t"/coefficient of "z"
hence, v= 10 m/s

2) wavelength, = 2/k

comparing the equation to (1): k= 2 rad/m

hence, = 2/k = meters = 3.1416 m.

3) frequency , w = 20 rad/s ( by comparing)

also, in HZ, frequency = w/2 = 3.18 Hz

4) amplitude of ELECTRIC FIELD ,E0 = e0 = 0.3 N/C ( by comparing)

5) the give wave is travelling in +ve z direction , as the co-efficient of z is -ve. AS the cross product of ELECTRIC FIELD VECTOR AND MAGNETIC FIELD INTENSITY VECTOR points in the direction of the travelling wave. And also , the electric field i sin + x direction.

therefore, to make the cross -product equal to +z, MAGNETIC FIELD INTENSITY VECTOR must be in + Y direction.

6)  MAGNETIC FIELD INTENSITY = E0 / = 0.3/0.01 = 30 AMPERE/METER

FOR PERMITTIVITY & PERMEABILITY:

= (/)................(1)

& v = 1/()..................(2) { velocity of the TEM is given by 1/()}

from (1) & (2)

= 0.03 Tm/AMPERE ( permeability)

& =3.16 FARADAY/meter (permeability)

7) relative permittivity :

r =  / 0 = 3.5 x 10^11

8) relative permeability :

r = /0 = 2.4 x 10^4

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