# Mumbai University Previous year question papers

## Electromagnetic Engineering

N.B.

Attempt any four questions out of remaining six  questions.

Figures to the right indicate full  marks.

Vector notations should be used wherever necessary.

Assume any suitable data whenever required but Justify the  same.

1.

(a) Derive the boundary condition for the normal and tangential components of electric and magnetic field. –

(b) Derive the wave equation for homogeneous, unbound source free medium starting from maxWell’s equation.

(c) A uniform plane wave in a medium having cr= 10- 3 slm, E = 80 EOand /-l= Ilo is having a frequency of 10KHz. Find velocity of wave, wavelength, a, p, 1′].

2.(a) State and prove Poynting theorem. Explain,the terms instantaneous, average and complex Poynting vector..

(b) In a non-magnetic medium

E = 4 sin (2Jt x 107t – 0.8x) az v 1m . Find-  (i) Er’ 1′]

(ii) The time average power carried by the wave.

3. (a) Derive the expression for the reflection and transmission coefficient for parallel polarised plane wave at oblique incidence.

(b) An EM wave travels in free space with the electric field component E = 100 ej (O.866y+ O.5z) ~x V/ m is incident on a dielectric medium having  cr = 0, E = 4 EO’ Il = Ilo and occupyingz ;:::0,

Calculate :-

(i) The angle of incidence, reflection and transmission

(ii) The reflection and transmission coefficients

(iii) The toal E field in fr~e space

(iv) The total E field in dielectric.

4.(a) Derive an expression for the input impedance of a two wire transmission line.

(b) A 2 m long lossless line has an impedance of 300.0. The velocity of propagation is 2.5 x 108 m/s. The load has an impedance of 300 n with sending end voltage being 60 V at 100 MHz. Find:

(i) The phase constant

(iv) The power delivered to the load

(v) The load reflection coefficient and standing wave ratio.

5. Explain briefly radiation from a short dipole in free space. Show that power radiated by the short dipole is PT = 80 Jt2 I~s . T . Hence obtain the expression for radiation resistance.

6.

(a) Derive the expression for the field components of a transverse electric wave propagating 12

through a rectangular waveguide.

(b) An air filled rectangular waveguide of inside dimensions 7 x 3.5 cm2 operates in the TE10  8 mode.  Find cut-off frequency ,

6.Determine guide phase constant of the wave in waveguide at operating frequency of 3.5 GHz.

Determine guide wavelength at the same operating frequency.

Find ‘Phase velocity’ of the EM wave.

7. Write short notes on any four :-

(ir Smith chart

(ii) Skin depth

(iii) Maxwell’s equation for time varying field

(iv) Surface impedance of conductor

(v) Concept of retarded potentials

(vi) Parallel plane waveguides.