Question

-21. Suppose a uniform plane wave is traveling in the negative x direction in a lossless medium of u u & = 9€, with the 5 V/m (rms) electric field in the +y direction. The wavelength of the wave is 2 m. (a) Determine the frequency in Hz and velocity in m/s of the wave, and the refractive index of the medium. (b) Write complete time-domain expressions of the electric and magnetic field vectors. Determine the rms value (in A/m) of the magnetic field H. (c) Calculate the ratio of the amplitudes of E and H along with the unit and confirm that it is equal to the intrinsic impedance of the medium.

Answer 1

Velocity of EM ware, or t racon - 28. of a velocity of light in freespace= 3x 10 ups ve 100 ms = 5 ] & Eola 5v/m Wavelength, a= 2 m (a) Frequency, afo 100 Hz = 5x10 Hz Velocity, v= 108 m/s Refractive index = c. 3x10 t = 3 (6) The equation for electrich field (E) E - Eo com (wł +ka) .com (284+ 25. x) The magnetic field (3) B = 8. Con (wtt kx) = Bo Con (20ft + 20 ) on the EM ware travelling. ve a direction. where, El = 54/m. (B) = L = 1.67x108 Am the direction of 8 is in-z-direction - B =_1-67x108 4 and 8 = 57 fa frequency = 5x10 Hz and a= 2m. . | 8 = 57x con 25 (5x10?t + 2 T B = -1.67 X100 êx conin (5x107t + x) RM I value of it is Bola 167 x 100 = 1.18*108 Ahm (c) The ratio of amplitudes of È and it will be (to la v = 100 ml Intrinsie impedence - 2- . det Tut Jacomo = 108 ml