1(a) transform the vector

**A**= y**a**_{x}– x**a**_{y}+ z**a**_{z}into cylindrical coordinates. (04 marks)
(b) Determine the electric field
intensity on the axis of a circular conductor (ring) of linear charge density ρ

_{L.}(06 Marks)
(c) Determine using gauss’s law,
the electric field due to a sphere of charge of radius, a. The charges are
uniformly distributed over a spherical surface with a distribution ρ

_{s. }(06 Marks)
(d) An infinitely long line
charge of uniform density, ρ

_{L}produces an electric field. Show that the divergence of this electric field is zero everywhere except at the line. (04 marks)
2(a) Write a note on
equipotential surface. (04 Marks)

(b) Three identical line charges
with ρ

_{L}= 10 nC/m are placed on each of the coordinate axes of a rectangular coordinate system. Given the points A(1,2,3) and B(8,6,10), find V_{AB}due to all the three line charges. (06 Marks)
(c) Show that the gradient of the
scalar field, V (x,y) = x-y (V) is normal to the planes of constant V. (05
Marks)

(d) What is an electric dipole?
Mention one application. (05 marks)

3(a) Ina cylindrical electron
beam of radius R and unit length, the volume charge density is given by, ρ

_{v }= Kρ, where K is some arbitrary constant. Determine the energy stored in the beam. (08 Marks)
(b) Distinguish between
convection current and conduction current. (06 Marks)

(c) A copper wire of cross
sectional area, 10

^{-4}m^{2}carries a uniformly distributed current of 200 A. If the electron density in copper is 4.25×10^{28}electrons/m^{3}, determine the average drift velocity of the electrons. What is the electric field in the wire? If the length of the wire is 10^{5}m, calculate the potential difference between its ends. What is the resistance of the wire? (06 Marks)
4 (a) Write a note on boundary
conditions for perfect dielectric materials. (06 Marks)

(b) Determine the capacitance of a parallel plate
capacitor consisting of two parallel conducting plates of area A and separation
d. (06 Marks)

(c) Find the capacitance of an
isolated conducting sphere of radius a. (04 Marks)

(d) What is Poisson’s equation?
Explain. (04 Marks)

5 (a) State and explain
Uniqueness theorem. (06 Marks)

(b) In a charge free region of
free space, the potential field is given as V (x,y) = x

^{3}-f(x)-y^{2}. Find f(x) if**E**and V are zero at (0,0,0). (06 marks)
(c) Determine magnetic field due
to a current, I flowing in a straight conductor of length 2L. (08 Marks)

6(a) Explain Ampere’s circuital
law. (04 Marks)

(b) Write down Maxwell’s
equations. (04 Marks)

(c) Show that the magnetic flux
density

**B**set up by an infinitely long current carrying conductor satisfies the Gauss’s law. (06 Marks)
(d) Write a note on scalar and
vector magnetic potentials. (06 Marks)

7 (a) Explain the terms magnetic
susceptibility and relative permeability. (04 marks)

(b) Find the self inductance per
unit length of an infinitely long solenoid. (04 Marks)

(c) A steady current is
restricted to flow on the outer surface of the inner conductor (ρ = a) and the
inner surface of the outer conductor (ρ = b) in a coaxial cable. If the coaxial
cable carries a current, I, determine the energy stored per unit length in the
magnetic field in the region between the two conductors. Assume that the
dielectric is non-magnetic. (06 Marks)

(d) Consider two coupled circuits
having self-inductances L

_{1}and L_{2}that carry currents I_{1}and I_{2}respectively. The mutual inductance between the two coupled circuits is M_{12}. Determine the ratio I_{1}/I_{2}that makes the stored magnetic energy, W_{m}a minimum. (06 Marks)
8 (a) From Faraday’s law, derive
Maxwell’s equation in point form. (04 marks)

(b) The dry earth has a
conductivity 10

^{-8}S/m and a relative permeability 4. Find the frequency range on which the conduction current dominates the displacement current. (04 Marks)
(c) Write the phasor and
time-domain forms of a uniform plane wave having a frequaency of 1 (GHz), that
is traveling in the +x direction in a medium of ε = 12ε

_{0}and µ = µ_{0}(06 Marks)
(d) What are Snell’s laws?
Explain. (06 Marks)

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