2. a) Derive the expression for electric field intensity due to a uniformly charged line. [5]

b) Given points A(8, -5, 4) and B(-2, 3, 2), find

i) The distance from A to the origin.

ii) The vector from A to B.

iii) The unit vector from A to B. [5]

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OR

3. a) State and prove Gauss's law. [5]

b) Find the electric field intensity at a point P(0, 0, z) due to a circular ring ? = a in the z = 0 plane if the ring carries a uniform charge ?_l C/m. [5]

4. a) Derive Poisson's and Laplace's equations. [5]

b) Determine the capacitance of parallel plate capacitor having a dielectric medium e_r1 = 1.5 for y < d/2 and e_r2 = 3.5 for y > d/2, if the capacitor has an area of A m² and a plate separation of d m. [5]

OR

5. a) Derive the expression for magnetic field intensity due to straight current carrying filament. [5]

b) Using Ampere’s circuital law, find H due to an infinite sheet of current with uniform current density K = K_y a_y A/m. [5]

6. a) Explain the concept of scalar and magnetic potential. [5]

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b) A conductor with cross-sectional area of 10 cm² carries a conduction current of 0.2 A. When the drift velocity of electrons is 5 × 10^-6 m/s, calculate the electron density. [5]

OR

7. a) Derive Maxwell's equations for time varying fields. [5]

b) In a lossless dielectric for which ? = 300p, µ_r = 1 and H = -0.2 cos (?t - z) a_x + 0.5 sin (?t - z) a_y A/m, calculate e_r, ? and E. [5]

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8. a) Explain the concept of wave polarization. [5]

b) Derive the expression for reflection coefficient and transmission coefficient for a wave incident normally on a dielectric. [5]

OR

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9. a) Explain about pointing theorem. [5]

b) A plane wave propagating through a medium with e_r = 8, µ_r = 2 has E = 0.5 sin(10⁸t - ßz) a_x V/m. Determine [5]

i) ß ii) The loss tangent iii) Wave impedance iv) Velocity v) H field.

10. a) Derive the expressions for voltage and current at any point on a transmission line. [5]

b) A lossless transmission line with Z₀ = 50 O is 30 m long and operates at 2 MHz. The line is terminated with a load Z_L = 60 + j40 O. If v = 0.6c on the line, find: [5]

i) The reflection coefficient G.

ii) The standing wave ratio s.

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iii) The input impedance.

OR

11. a) Explain single stub matching with relevant expressions. [5]

b) A 70 O lossless line has s = 1.6 and maximum voltage magnitude of 4.2V. Find [5]

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i) V_min ii) Z_L if the line is 0.6? long.