# RGPV Exam Papers

## Electromagnetic Theory Dec 2005

Note:      Attempt any five questions/Problems.

1   (a) Write expression for incremental length, surface and volume in Cartesian, cylindrical and

spherical co-ordinate system.

(b) State the explain divergence theorem and stoke’s theorem.

2   (a) Find the nature of the field :

F= (150/r2) Ř›………+10……. +5ž

(b)  Using the Gauss law in differentia from, obtain the electric filed intensity at different point due

the following charge distribution in spherical co-ordinates  :

p(r,θ,Ф)=  p0 {r/a} 0 < r < a

=   0           a < r < g

3.  (a) A circular disc has uniform charge distribution of density of pc/m2 . Calculate electric field along

its axis. Radius of disc is a meters.

(b) Find energy stored in the electrostatic field for a charge distribution with spherical symmetry has

volume charge density:

P = p0           0 ≤ r ≤ a

= 0               r > a

4. (a) State and explain Biot – Savert ‘s law.

(b) A circular loop of wire of radius ‘a’ lying in xy-plan with its centre at the origin carries a current

I amp., in the direction . Calculate magnetic fields intensity along z-axis.

5. (a) Write Maxwell’s equation in generalize form.

(b) Starting from basic principle obtain an basic expression for magnetic vector potential.

6. (a) Obtain boundary conditions for magnetic field.

(b) Derive Maxwell’s equation from Ampere’s law and explain its modification .

7.     Explain /Define the following :

(i)   Intrinsic impedance

(ii)   Velocity of wave propagation

(iii)  Uniform plane wave (E-M wave)

(iv)  Polarization of wave (E-M wave)

(v)  Scalar magnetic potential

8.(a) A lossless dielectric medium has σ =0, µr = 1 and εp = 4 . An electromagnetic wave has magnetic

fields expressed as :

H =-0.1cos (ωt-z) x + 0.5sin (ωt-z) y A /m

Find (i) phase constant (ii) angular (iii) wave impedance (iv) the components of electric field intensity

of the wave.

(b)  State and explain pointing theorem.