**RGPV Question Papers **

**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 a_{x} +20x^{2}a_{y }+ 2a_{z} V/m . Calculate V_{PQ },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=5x^{3}+ f(x) -2 y^{2}.

(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 ε_{r1 }=2.5,while the region z> 0 is

characterized

by ε_{r2}= 4 . Let E_{t1 }= -30 a_{x} +50 a_{y} +70 a_{z} V/m . Find :

(i) E_{t1} (ii) D_{2 }(iii) P_{2} and (iv) θ_{2 }.

(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

edge or sharp edge ? Justify your answer .

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 a_{y} T and velocity v= 2.5 sin 1000 a_{z} 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 Ē_{s} =200 e ^{–j.01z-}a_{x} 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 ε_{r1=}8,µ_{r1} =1 and σ_{1}= 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.