# Mumbai University Previous year question papers

Table of Contents

## IV Sem ETC-Examination Dec 2009

## Electromagnetic Wave Theory

N.B.: QuestionNO.1is compulsory,

(2) Attempt any four from remaining six.

(3) Assume any suitable data if required.

(4) Figures to right indicates full marks.

1. Solve any four :-

(a). Convert P (1°’ ~ ‘ 😉 in cylindrical.

(b) State and prove Gauss’s law.

(c) What is energy density in electrostatic field write its formula.

(d) Show that energy store in parallel plate capacitor is ~2 CV2

(e) *State and explain Amp.ckt law.*

2. (a) It is required to hold 3 equal point charge of +Q each in equilibrium at the corner of an equilateral triangle. Calculate the point charge which will do this if placed at the centre of a triangle.

(b) A charge density es = 0.5 nc/m2 covers the infinite plane -x + 3y – 6z – 6 m. Find electric field intensity on the side containing the origin.

3. (a) Given that D =*30e.*a~r/b – 2 ~ az (c I m2) in cylindrical co-ordinates, find the outward flux crossing the right circular cylinder described by r = 2b, Z = 0 and Z = 5b (m).

(b) Find the work done in moving a point charge Q = 10 ~C from origin to the point (3m, ;, 😉 in spherical co-ordinates. The equation of field is E= 10ra + ~ . a”, (vim).r rSln8 ‘I’

4. (a) A total charge of 3″ nc is uniformly distributed over a circular ring of rai 2 m placed on z = ° plane with center at origin. Find electric potential at (0, <\>, 5).

(b) Derive the equation of potential interms of dipole moment.

5. (a) Write short note on scalar and vector magnetic potential.

(b) State uniqueness theorem and give its proof.

6.(a) Define Poynting vector. Obtain integral form of Poynting theorem and explain each term.

(b) Explain significance of Maxwell’s equation. Also explain the concept of displacement current or current density.

‘7.(a) Given that the electric field intensity of an electromagnetic wave in non-conducting dielectric medium with permittivity L = 9LO and permeability IlO is E(z,t)= 8.y5 cOS(109t- ~z)v1m Find the magneticfield intensity H and the value of.

(b) Explain depth of penetration (Skin Depth). Find the skin depth at frequency 1.6 MHz in Aluminium whose cr= 38.2 Mslm anp Ilr= 1.0. Also finqpropagation constant and wave velocity in this medium (Assume a = 13=*1/8)*