Reference no: EM132507003

Question 1.

In Fig. 1, the dielectric sphere of radius R₀ = 1 m is filled uniformly with charge and the volume charge density is Ρ_v = 1 mC/m³. Also, the relative permittivity for the sphere is 2. The sheet y =3 m (parallel to x-z plane) is infinite in extent and the surface charge densities Ρ_s = -1 mC/m^2. Figure out the electrical filed intensity at the marked locations A, B and C. (Here are the reference formulae: ds^_R  = R^R²sinθdθdΦ, and dv = R²sin θdRdθdΦ)

Question 2. the loop shown in Fig. 2 moves away from a wire carrying a current I₁ = 10 cos(2Πt) Ampere at a constant velocity u^→= yˆ5 m/s. If R=10 Ω , find I 2 as a function of t. Let's assume that y₀=0 at t=0.

Question 3. An uniform plane EM wave is traveling in the +z direction inside a lossless media with properties μr and εr, and obeys the following equations:

Vector phasor E~(x, y, z) = E~(z) =xˆEx(z)~

∂Ex(z)/∂z² + k²Ex (z) = 0

1). Express the intrinsic impedance, phase velocity, and the wavelength.
2). Express E~x (z) assuming | E~x (z = 0) | = 0.1 V/m
3). Express H~ (x, y, z)
4). Calculate the instantaneous electrical and magnetic fields assuming μr = 1, εr = 2, initial phase for the electrical field = π, and time frequency = 50 THz (Tera Hz).
5). What are the instantaneous power density and the average power density carried by the wave?

Question 4. Refer to our textbook

Derive the wave equations of eq. (12.5) starting from the discrete-space models on page 577. This will need to include the explanation of (1) the lumped element discrete-space model in Fig. 12.1, (2) the derivation of the discrete-space equations (12.1) and (12.2), and (3) the detailed derivation of eq. (12.5) from (12.3).

Question 5. A 1.05 GHz generator circuit with series impedance Z_g = 10 Ω and voltage source is vg(t) = 10cos(ωt - 600) (V) is connected to a load with impedance (100+j50) Ω via a 67-cm long lossless transmission line. The phase velocity of the line is 0.7c where c is the speed of light in vacuum. Find the complete solution of d(z, t) and s^(z, t) on the line.