# 4th Sem Electromagnetic Theory June 2005

Note:      Attempt any five questions. All question carry equal marks.

1   (a) State Gauss law, use in to determine electric filed intensity due to a uniform surface charge

of infinite size.

(b) Given the electric filed, E=40xy ax +20x2ay + 2az V/m . Calculate VPQ ,given that P (1,-1,0) and

Q(2,1,3) .

2  (a)   In a charge free region of free space, a potential field is given as :

V(x,y0=5x3+ f(x) -2 y2.

(b)  Drive an expression for energy density of stored energy in electric filed and from it find how

much energy is store in a parallel plate capacitor .

3        (a)  Region z≤0 contains a perfect dielectric for which εr1 =2.5,while the region z> 0 is

characterized

by εr2= 4 . Let Et1 = -30 ax +50 ay +70 az V/m . Find :

(i) Et1    (ii) D2    (iii) P2 and   (iv) θ2 .

(b)    A conductor is placed in static electric field in air (i) What will be the electric field inside the

conductor, justify your answer . (ii) What will be the electric field at the interface of air and

conductor ? (iii) Will there be any charge on conductor surface, if yes, will it be more at round

4   (a)       Define curl of a vector field and an expression for curl of magnetic filed  H.

(b)       A distribution line consists of straight parallel conductors supported on the cross arms of

wooden  poles space 100m apart . The normal spacing between the two conductor is 20 cm. A

current of  10000 A flows down one conductor  and back the other during a fault . Drive an

expression for  force between the conductor  and calculate the same .

5   (a)    Define magnetic dipole moment magnetization vector and establish a relation between filed

magnetic filed intensity , magnetic flux density and magnetization vector.

(b)    Write a short note on vector magnetic potential.

6   (a)   A straight conductor of 0.2 m lies on the x-axis with one end of origin. The conductor is subjected

to a magnetic flux density  B= 0.04 ay T and velocity v= 2.5 sin 1000 az m/s . Calculate the motional

electric field intensity and e.m.f. induced in the conductor .

(b)   Write Maxwell’s  equations in point from  for time varying fields and explain the meaning behind

them.

©    Calculate the self –induction and the mutual inductances between two coaxial solenoids of radius 2

cm and 3 cm with turns /m 50 and 80 respectively .

7   (a)  Explain phenomenon of wave propagation in dielectric medium for sinusoid ally time varying

uniform plan wave . Discuss attenuation coefficient , complex permittivity ,loss tangent , phase

constant, phase velocity ,wavelength and characteristic impedance .

(b)   A uniform plan wave in free space is given by  Ēs =200 e –j.01z-ax V/m . Find the instantaneous  value

of  pointing vector at (i) t=0, z =15 and 45m (ii) z=0, t = 40 and 120 ns.

8   (a) Determine the amplitudes of reflected and transmitted E and H fields at the interface between

two regions . The characteristics of region are εr1=8,µr1 =1 and σ1= 0, region 2 is free space . The

incident E+0 in region is 1 is of 1.5 V/m . Assume normal incidence . Also find the average power in

two regions .

(b)  Define surface impedance as referred to the electric over a conductor surface drive an expression

for it .  For a perfect conductor, relate it to skin a depth.