1(a)
Transform the vector

**B**= y**a**– x_{x}**a**+ z_{y}**a**into cylindrical co-ordinates. (4 Marks)_{z}
(b)
Derive an expression for electric field due to an infinite sheet of electric
charge. (6 Marks)

(c)
Explain Gauss’s law. Mention one application. (6 Marks)

(d)
Find div D at the origin if

**D**= e^{-x}sin y**a**_{x}– e^{-x}cos y**a**_{y}+ 2 Z**a**_{z}. (4 Marks)
2
(a) Write notes on potential gradient and electric field due to dipole. (8
Marks)

(b)
Deduce a relation for the work done in moving a point charge in an electric
field. (4 Marks)

(c)
Write a note on ‘the method of images’. (4 Marks)

(d)
The electron and hole mobilities of a semiconductor are 0.43 and 0.21 m

^{2}/volt.sec at a particular temperature. If the electron and hole concentrations are both 2.3× 10^{19}m^{-3}, find the conductivity at this temperature. (4 marks)
3
(a) What are the boundary conditions for perfect dielectric materials? (6
Marks)

(b)
Deduce the capacitance of a two-wire line. (10 Marks)

(c)
Determine the dielectric constant of a material in which the electric flux
density is 4 times the polarization. (4 Marks)

4
(a) Derive Poisson’s and Laplace’s equations. (6 Marks)

(b)
Explain how Laplace’s equation can be solved through numerical iteration. (8
Marks)

(c)
The four sides of a square trough are held at potentials 0, 20, -30 and 60
volt. The highest and lowest potentials are kept on opposite sides. Determine
the potential at the centre of the trough. (6 Marks)

5
(a) What is Ampere’s circuital law. (4 Marks)

(b)
Write a note on Stoke’s theorem. (4 Marks)

(c)
Differentiate between scalar and vector magnetic potentials. (8 Marks)

(d)
A filamentary conductor is formed into an equilateral triangle with sides of
length ‘l’ carrying current ‘I’. Determine the magnetic field intensity at the
centre of the triangle. (4 Marks)

6
(a) Explain self inductance and mutual inductance. (6 Marks)

(b)
What are retarded potentials? (4 Marks)

(c)
Write Maxwell’s equations in point form and in integral form. (6 Marks)

(d)
A ferrite material is operating in a linear mode with B = 0.05 T. If m

_{r}=50, calculate M, H and c_{m}. (4 Marks)
7
(a) Write a note on lossless propagation of sinusoidal voltages. (6 Marks)

(b)
What is skin effect? Derive a relation for skin depth. (6 Marks)

(c)
Write a note on wave polarization. (4 Marks)

(d)
A 50 Ω lossless transmission line is terminated by a load impedance, Z

_{L}= 50 – j75 Ω. If the incident power is 100 mW, find the power dissipated by the load. (4 marks)
8(a)
What is chromatic angular dispersion? (4 Marks)

(b)
Write a note on planar dielectric waveguides. (6 marks)

(c)
Write a note on radiation of electromagnetic energy from a simple dipole
antenna. (6 Marks)

(d)
An optical fiber link is known to have dispersion β

_{2}=20ps^{2}/km. A Gaussian light pulse at the input of the fiber is of initial width T = 10 ps. Determine the width of the pulse at the fiber output if the fiber is 15 km long. (4 Marks)
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