# Electromagnetic Theory Dec 2004

Note:Attempt any five questions.

All question carry equal marks.

Assume suitable data wherever

necessary.

1 (a)      State gauss law and prove that V.D= pv.

(b)   (i)  Transform a vector  A= ya­x –x.ay+z.az into cylindrical coordinates .

(ii) Obtain electric field in all regions due to following charge distribution in free space :

P(rФz) =0,0<r<a

= p0, a<r<b

= 0, b<r<

2  (a) Drive the relation for energy stored in electro –static field .

(b) State and prove stake’s theorem.

3  (a)  Explain electronic polarization and drive the equation D= E+P.

(b) Prove Poisson’s and Laplace equation starting from point from of Gauss law .

4  (a)  State and prove ampere’s circuital law. What is the application of this law?

(b) A rectangular current loop in the z =0 plan has corners at (0,0,0) ,(1,0,0), (1,2,0) and (0,2,0). The

loop carries a current of 5 Amp in ax direction . Find the total force and torque on the loop

produced by the magnetic fild B= (2ax+ 2ay -4a­z) eb/m2 .

5  (a)  State and prove magnetic boundary conditions .

(b)  Using the concept of vector magnetic potential , find the magnetic flux density at a point due to a

long  straight  filamentary conductor carrying a current  I in az direction .

6  (a) Drive the expression for self inductance of solenoid .

(b) Drive the Maxwell equation V×E= – ­ B t and express all the Maxwell’s equation in integral from .

7  (a) Determine the relation between E and H in a uniform plane wave .

(b) A distortion less line has characteristic impedance of 60  ,Attenuation constant α =20 m Np/m,

wave velocity is 3/5 times that of light . Find parameters of transmission line the and wavelength

at frequency of 100 MHz .

8   Write short note of any two of the following  :

(i) Pointing   vector        (ii) Ohm’s Law in point from      (iii) Polarisation of waves