1(a) A uniform volume
charge distribution exists in a spherical volume of radius a. Using the concept
of energy density or otherwise, find the
total energy of the system. (6 Marks)

(b) Three charges -1(µC), 4(µC) and 3(µC) are located in
free space at (0,0,0), (0,0,1) and (1,0,0) respectively. Find the energy stored
in the system. (4 Marks)

(c) Transform the vector

**A**= y**a**_{x}– x**a**_{y}+ z**a**_{z}into cylindrical co-ordinates. (4 Marks)
(d) The electric potential in the
vicinity of the origin is given as V = 10x

^{2}+ 20 y^{2}+ 5 z^{2}(V). What is the electric field intensity? Can this potential function exist? (6 Marks)
2(a) Determine the capacitance of
a parallel-plate capacitor consisting of two parallel conducting plates of area A and
separation d. (6 Marks)

(b) Using Laplace’s
equation, obtain the potential distribution between two spherical conductors
separated by a single dielectric. The inner spherical conductor of radius ‘a’
is at a potential ‘V

_{0}’ and the outer conductor of radius ‘b’ is at potential 0. Also find variation of**E**. (8 Marks)
(c) A cubical region of space is
defined by the surfaces x=1.8, y=1.8, z=1.8,x=2, y=2 and z=2. If

**D**=3y^{2}**a**_{x}+3x^{2}y**a**_{x}(C/m^{2});
(i) Find the exact value of the
total charge enclosed within the cube by surface integration.

(ii) Find an appropriate value
for the enclosed charge by evaluation of derivatives at the centre of the cube.
(6 Marks)

3(a) State Ampere’s circuital
law. (4 Marks)

(b) State Stoke’s theorem. (4
Marks)

(c) Show that the magnetic flux
density B set up by an infinitely long current-carrying conductor satisfies the
Gauss’s law. (4 Marks)

(d) A cylinder of radius ‘b’ and
length ‘L’ is closely and tightly wound with N turns of a very fine conducting
wire. If the wire carries a dc current I, find the magnetic flux density at any
point on the axis of the cylinder (solenoid). What is the magnetic flux density
at the centre of the cylinder? Also, find

**B**at the ends of the cylinder. (8 Marks)
4(a) Write a note on magnetic
torque and moment on a closed circuit. (6 Marks)

(b) What are magnetic circuits?
Distinguish between linear and non-linear magnetic circuits. (10 Marks)

(c) Through a suitable experiment
on a magnetic material, the magnetic flux density B is found to be 1.2 T when
H=300 A/m. When H is increased to 1500 A/m, the B field increased to 1.5 T.
What is the percentage change in the magnetization vector? (4 Marks)

5(a) Find the self-inductance per
unit length of an infinitely long solenoid. (6 Marks)

(b) A steady state 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. (8 Marks)

(c) 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}. Find the ratio I_{1}/I_{2}that makes the stored magnetic energy W_{m}a minimum. (6 Marks)
6(a) State Faraday’s law. Derive
Maxwell’s equation in point form from faraday’s law. (8 Marks)

(b) Show that for a sinusoidally
varying field, the conduction current and the displacement current are always
displaced by 90

^{0}in phase. (4 Marks)
(c) The dry earth has a
conductivity 10

^{-8}S/m, and a relative permittivity 4. Find the frequency range on which the conduction current dominates the displacement current. (4 Marks)
(d) Write Maxwell’s equations in
integral form. (4 Marks)

7(a) Derive the differential form
of continuity equation from the Maxwell’s equations. (4 Marks)

(b) Write the set of four
Maxwell’s equations in terms of eight scalar equations in Cartesian
coordinates. (12 Marks)

(c) Consider the wet earth with
the following properties: ε = 30 ε

_{0 }μ = μ_{0}σ = 10^{-2}S/m. Determine the ratio of amplitudes of conduction and displacement currents at 100 MHz. (4 Marks)
8(a) Write the phasor and
time-domain forms of a uniform plane wave having a frequency of 1 GHz, that is traveling
in the +x=direction in a medium of ε = 12ε

_{0}
μ = μ

_{0}. ( 6 Marks)
(b) Define skin depth. Prove that
high frequency resistance is very much greater than dc resistance. (6 Marks)

(c) State and explain Poynting’s
theorem. (5 Marks)

(d) Determine the critical angle
if the refractive index of the medium is 1.77. (3 Marks)

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