Question

1. The magnetic field of a wave propagating through a certain nonmagnetic material is given by H-x30cos(10%-0. Sy) (mA/m) Find the following: (a) The direction of wave propagation. (b) The phase velocity (c) The wavelength in the material. (d) The relative permittivity of the material (e) The electric field phasor 2. A 60-MHz plane wave traveling in the -x-direction in dry soil with relative permittivity &4 has an electric field polarized along the z-direction. Assuming dry soil to be approximately lossless, and given that the magnetic field has a peak value of 10 (mA/m) and that its value was measured to be 7 (mA/m) att0 andx- -0.75 m, develop complete expressions for the wave's electric and magnetic fields 3. An RHC-polarized wave with a modulus of 2 (V/m) is traveling in free space in the negative z- direction. Write the expression for the wave's electric field vector, given that the wavelength is 6 cm. 4. Plot the locus of E(0, t) for a plane wave with Determine the polarization state from your plot. 5. For each of the following combinations of parameters, determine if the material is a low-loss dielectric, a quasi-conductor, or a good conductor, and then calculate α, β , λ , up, and ηc (a) Glass with μ 1, ε,-5, and σ-10-12 S/m at 10 GHz. (b) Animal tissue with μ,-1, &-12, and σ = 0. 3 S/m at 100 MHz. (c) Wood with μ.-1, ε,-3, and σ 10-4 S/m at 1 kHz.

Answer 1

H = 30 cos(10^8 t - 0.5 y) a^^_z mA/m H = H_0 cos(wt - beta y) a^^_z By comparing above two equations w = 10^8 beta = 0.5 (a) Wave propagating in positive �y� direction (b) Phase velocity v_p = w/beta = 10^8/0.5 = 2 times 10^8 m/s (c) lambda = VP/f = 2 times 10^8/10^8/2 pi lambda = 4 pi m (d) VP = 1/squareroot mu_0 epsilon_0 epsilon_r = 3 times 10^8/squareroot epsilon_r = 2 times 10^8 epsilon r = 2.25 (e) nu = 120 pi times 1/squareroot epsilon r = 120 pi/1.5 = 80 pi -Ex/Hz = nu = Ez/Hx = > E_x = nu + 1/E_x = -80 pi times 30 cos(10^8 t - 0.5 y) a^^x