# Mumbai University Previous year question papers

## IV Sem ETC-Examination Dec 2007

## Electromagnetic Wave Theory

N.S. : (1) Question No.1 is compulsory.

(2) Answer any four out of the remaining six question.

(3) Assume suitable data if necessary.

(4) Figures to right indicates full marks.

1. Attempt any four of the following:-

(a) State and explain the divergence theorem.

(b) Explain the. need for modification of Ampere’s law for time varying fields.

(c) Explain the concept of Electric scalar potential.

(d) Explain Ampere’s circuital law.

(e) State the Maxwells equation for static fields.

2. (a:) Derive an expression for the Electric field intensity due to an infinite line charge. 10

(b) A uniform line charge, PL = 25 nclm lies on the line X=-3,’ Z = 4 in free space. 10

Find E in Cartesian components at the point P(?, 15, 3).

3. (a) If D= 4xya x + 2(x2 + z2)ay + 4yzaz *c/m2. *

Evaluate surface integral to find the total charge enclosed in the rectangular parallelopiped 0< X < 2, 0 < Y < 3,0 < z < 5 m.

(b) If E =– 8xy ,ax -, 4X2ay + az v / m. Find the work done in carrying a 6 coulombs charge from A(1, 8, 5) to B(2, 18, 6) along the path y=3x + 2, z =x + 4.

4. (a) A potential function is V=2x + 4y volts in free space. Find the stored energy in free space in the 1m3 volume centered at the origin.

(b) V=0 volts’ for r =O.1m and V + 100 volts for r =2.0m in spherical co-ordinates. Assuming free space bet~een the concentric spherical shelts, find E& Dusing Laplace’s equation.

5. (a) Using Biot Savart law, find the magnetic field intensity due to an infinitelong straight filament placed along z-axis.

(b) A square filamentary loop 2 meters in side is placed in Z = 0 plane with its center ‘”at origin. If current of 10 A is passing through loop, find H at origin.

6.- (a) State and explain Maxwell’s equation for free space in time varying fields. 10

(b) The circularloop conduction lies inthe z=0 pla.ne,has a radius of 0.1 mand resistance of 5.00. Given B =0.20 sin 103t a * iT), *determine the current in the loop.

7.(a) For a electromagneticwave prove that E . H= 0 and E x His having the direction of-propagation of wave. .’

(b) Calculat.e the intinsic impedance 11, the propagation constant “(, and the wave .velocity J..l for a conducting medium in which 0″ =58 Mslm, J..ly= 1, at a frequency,f= 100 MHz. .