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INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

1 (a) State and explain the Coulomb's law of force between the two point charges.
5 M
1 (b) Four 10nC positive charges are located in the Z=0 plane at the corners of a square of side 8cm. A fifth 10nc positive charge is located at a point 8cm distant from the other charges. Calculate the magnitude of the force on the fifth charge in free space.
7 M
1 (c) A 100nc point charge is located at A(-1, 1, 3) in free space.
i) Find the locus of all points P(x, y, z) at which Ex=500 V/m.
ii) Find y1 it P(-2, y1, 3) lies on that locus.
7 M

2 (a) Determine the work done in carrying a charge of 2C from B(1, 0, 1) to A (0.8, 0.6, 1) in an-electric field E=ya, +xa, +2a, V/mt along the short arc of circle x2+y2=1, Z=1.
6 M
2 (b) Show that electrical field intensity is a negative potential gradient.
4 M
2 (c) Derive an expression for continuity equation in point form.
4 M
2 (d) The Z=0 defines the boundary between free space and dielectric medium with dielectric constant 20. The electric field intensity in free space is E=10a, +20a, +40a, V/mt. Determine the electric field intensity in the dielectric medium.
6 M

3 (a) Derive Poisson's and Laplace's equation.
6 M
3 (b) In free space volume charge density $\rho_s = \dfrac {200\epsilon _0}{r^{24}} C/m^3 ,$ use poison equation to find the potential V(r).
8 M
3 (c) Using Laplace's equation derive an expression for capacitance of parallel plate capacitor.
6 M

4 (a) State and explain Biot-Savart law.
6 M
4 (b) Prove that Ampere's circular law $\overrightarrow{\nabla} \times \overrightarrow{H} = \overrightarrow{J}$
7 M
4 (c) Determine the magnetic field intensity \( \underset{H}{\rightarrow}) at point P(0.4, 0.3, 0). If the 8A current in a conductor inward from ∞ to origin on the x-axis and outward to ∞ along y-axis.
7 M

5 (a) Deduce the expression for forces between differential current elements.
10 M
5 (b) A loop has a dimension of 1mt × 2mt and lies in the uniform magnetic field $\underset{B_B}{\rightarrow}=-0.6\overline{a}, + 0.8 \overline{a}, T.$ The loop current is 4mA. Calculate the torque on the loop.
10 M

6 (a) Using Faraday's law derive an expression for emf induced in a stationary conductor placed in a time varying magnetic field.
4 M
6 (b) In a certain dielectric media the relative permittivity ?r=5, conductivity ?=0, the displacement current density $\underset{J_d}{\rightarrow}=20 \cos (1.5 \times 10^R t-bx)\widehat{a}y \ \mu A/m^2.$ Determine the electric flux density and electric field intensity.
6 M
6 (c) Show that, in a capacitor the conduction current density is equal to displacement current density for the applied voltage of v(t)=va cos wt.
10 M

7 (a) Using Maxwell's equation derive an expression for uniform plane wave in free space.
8 M
7 (b) Derive an expression for propagation constant, intrinsic impedance and phase velocity in good conducting media if the uniform plane wave is propagating.
6 M
7 (c) The \( \underset{H}{\rightarrow}) field in free space is given by $\underset{H}{\rightarrow}(x.t)=10 \cos (10^3 t-\beta x) \widehat{a}y \ A/mt.$ Find β λ and E(x,t) at P(0.1, 0.2, 0.3) and 1=1ns.
6 M

8 (a) Derive an expression for reflection and transmission coefficient if the uniform plane wave incident normally at the boundary with different dielectric.
10 M
8 (b) Write a short note on Poynting theorem.
10 M

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