Test Paper - Electromagnetic Wave - Mumbai University - Electronics and Telecommunication - 4th Sem., Study notes of Electromagnetism and Electromagnetic Fields Theory

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P4-Exam.-Oct-09-

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Con. 5828-

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'6 () (3 Hours)

""'--N.B.: QuestionNO.1 is 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 CV

(e) State and explain Amp.ckt law.

SP-

[Total Marks: 100

31 /;2-/ o-~

..2- :3 0 d-e> S'~ 3 6 f""1"'.

20

2. (a) It is required to hold 3 equal point charge of +Q each in equilibrium at the corner 10

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 10 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 10

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 10

(3m, ;, ;) in spherical co-ordinates. The equation of field is

E = 10ra r + ~rSln8. a", (vim).'I'

40

4. (a) A total charge of 3" nc is uniformly distributed over a circular ring of rai 2 m placed 10

on z = ° plane with center at origin. Find electric potential at (0, <>,5). (b) Derive the equation of potential interms of dipole moment. 10

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. 10

(b) Explain significance of Maxwell's equation. Also explain the concept of displacement 10 current or current density. '

7. (a) Given that the electric field intensity of an electromagnetic wave in non-conducting 10

dielectric medium with permittivity L = 9LO and permeability IlO is

E(z,t) = 8.y5 cOS(109t- ~z)v1m Find the magnetic field intensity H and the

value of ~.

(b) Explain depth of penetration (Skin Depth). Find the skin depth at frequency 10

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)