# Mumbai University Previous year question papers

## IV Sem ETC-Examination June 2009

## Electromagnetic Wave Theory

NB.:-

1. Question No.1 is compulsory.

2. Attemptany four questions out of remaining six questions.

3. Assume any suitable data if required.

4. Figures to right indicates full marks.

1. Solve the following:-

(a) Convert p(3, 45°, 60°) in

(i) Cartesian

(iiL Cylindrical co-ordinate system.

(b) If \7–x V =O. Find constant a, band c. So that – *1\ 1\ 1\*

V=(x + 2y + az) ax + (bx ~ 3y – z) ay + (4x + cy + 2z)az is irrotational.

(c) State Coulombs Law in Electrostati.cs.

(d) Explain Method of Images.

2. (a) Find Electric field intensity due to infinite line charge.

(b) A spherical charge distribution is given by–

E at -=0.745..a

3.(a) Prove that the divergence of electric field and that of electric flux density in a charge free region is zero.

(b) Atotal charge of 3 hc is uniformlydistributed over a circular ring of radi 2 m placed on z

=0 plane with center at origin. Find electric potential at (0, 0, 5). Find

4. (a) State Uniqueness Theorem and give its proof.

(b) Prove that a static electric field is irrotational and the static magnetic fie~pis solenoidal.

5. (a) Derive formula to find Magnetic intensity due to infinite long straight conductor on z-axis by Biot-Savart’s law.

(b) State Ampere Circuital Law and find H due to straight current carrying conductor on Z axis at point P.

6. (a) Explain Scalar and Vector Magnetic potential.

(b) Define poynting vector. Obtain the integral form of poynting theorem and explain each term.

7. (a) A 10 GHz plane wave travel~ng in free space has an amplitude Ex == 10 VIm. Find V, A., ~ and TJ also find H.

(b) What is Wave Impedance or Intrensic Impedance ? Calculate wave impedance for free space.