1.a. Starting with Maxwell’s equations derive the expression for the wave equation for an electromagnetic wave propagating in a perfect dielectric.

1.b. Derive the Poisson’s and Laplace’s equation.

1.c. Explain the Dirichlet-type, Neumann-type and mixed boundary conditions.

1.d. Explain the radiation intensity, directivity and directive gain of the antenna.

1.e. State and explain Columb's law. point charges 1mC and -2mC are located at (2,3,-1)m and (-2,-1,4)m respectively. Calculate the electric force on a 10nC charge located at (0,3,1)m.

2.a. Derive Maxwell's equations in integral & Point form for time varying fields.

2.b. Define and explain skin depth. Derive the expression for the kin depth. Calculate the skin depth and velocity of propagation for a uniform plane wave at frequency of 100MHz travelling in aluminum. $\epsilon_{r}=1, \mu_{r}=1, \sigma=3.5 \times 10^{7} \mathrm{S} / \mathrm{m}$

3.a. Explain Poynting vector. Derive Poynting theorem and describe significance of each term.

3.b. Use the finite difference method to calculate the potentials at nodes 1 and 2 in the potential system shown in figure using iteration method and band matrix method.

4.a. Derive the expression for radiation resistance in far field region of an infinitesimal dipole.

4.b. Find the directive gain and directivity if $U(\theta, \phi)=10 \sin \theta \sin ^{2} \phi, \quad 0\lt\theta\lt\pi, 0\lt\phi\lt2 \pi$]

4.c. An antenna has a field pattern given by $E(\theta)=\sin ^{2} 2 \theta$ for $0\lt\theta\lt\pi$ Find the half power beamwidth and thefirst null beamwidth.

5.a. Explain sky wave propoagation. Calculate the skip distance for the flat earth with MUF of 20MHz if the wave is refleced from a height of 200km where the maximum value of refractive index of the earth is 0.95.

5.b. What is line of sight propagation? Obtain expression for range of line of sight for space wave propagation in terms of antenna's transmitting and receiving heights.

6.a. A transmission line is lossless and 0.25m long. It is terminated in a load of $\mathrm{Z}_{\mathrm{L}}=50+\mathrm{j} 25 \Omega$ at a frequency of 10MHz. The inductance and the capacitance of the line are12.5$\mu \mathrm{H} / \mathrm{m}$ and 5 $\mathrm{nF} / \mathrm{m}$ respectively. Use Smith chart to find the reflection coefficient, VSWR, the input impedance at the source.

6.b. Find the characterisitc impedance and propagation constant of a transmission line if $\mathrm{R}=4 \Omega / \mathrm{m}, \mathrm{L}=6 \mathrm{nH} / \mathrm{m}, \mathrm{G}=0.8 \mathrm{mU} / \mathrm{m},$ and $\mathrm{C}=0.3 \mathrm{pF} / \mathrm{m}$ the operating frequency of the transmission line is 100MHz.

6.c. Derive the expression for the input impedance of a transmission line.