# Electromagnetic Theory June 2004

Note:  Attempt any five questions.

All question carry equal weight age of marks.

1   (a)  State gauss law and use in to e

lectric intensity at appoint P laying at a distance ‘d’ from an infinite

straight wire uniformly charged . The charge per unit length =QL .

(b) If the spherical volume charges density distribution is given by:

Qv =Qv (1-r2/a2);r <a

=zero for r<a

Calculate the total Q.

2   (a) Given the field –

E= 40xyax +20x2-ay + 5az volt /m

Calculate VPQ given –

P (1,-1,0) and Q(2,2,2).

(b)    Prove Laplace and Poisson’s equation and show that they have unique solution .

3   (a)  State the prove divergence thermo. Explain its applications, giving examples.

(b)   Discuss the nature of electric filed at the interface of two dielectric materials.

©     Explain Maxwell’s equation in integral from and their significance.

4  (a)    Drive an express for the force between two linear paler long conductor of length  L carrying

opposite current of magnitude  I­1 and I2 assuming the distance between conductor = R.

(b)      Two identical circular loops of conductor of 1 m loop diameter, each carrying current of 100 A

placed closed to each other. Find the approximate of a attraction/repulsion between the two

loops.

5   (a)   Define the following –

Phase shift, Wavelength and propagation constant. Explain what do you mean by intrinsic

impedance.

(b)          The electric field intensity of an electromagnetic wave in free space is given by Ex = 0, Ez= 0

Ѐ{ω(t-z/v)}. Determine the expression for the component of magnetic intensity, H.

6     A       10 GHz plane wave travelling in free space has an amplitude Ex =10 V/m, find :

(i)  The phase velocity, wavelength and propagation constant.

(ii) Determine the characteristic impedance of the medium.

(iii) Find the amplitude of the magnetic field intensity.

(iv) Report part (i)if the waves is travelling in a losses unbounded medium which has

permeability of the same value as free space but permittivity is 4 time as that of free space .

Which has permeability so the same value a free space but permittivity is 4 time that if free

space.

7             Write explanatory brief notes on any three of the following:

(i) Vector magnetic potential

(ii) Retarded vector potential

(iv) Instantaneous average and complex pointing vector

(v)   Significance of continuity equation

8       Explain the phenomenon of reflection when a plan electromagnetic waves is incident on the

surface of a perfect dielectric. Define reflection coefficient. Compare the from of incident wave and

reflected wave.

Find the reflection and transmission coefficient of an electric filed wave travelling in air and

incident on a boundary between air and a dielectric having permeability = µ0 and permittivity =5 .

Find the average power.