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MU Electrical Engineering (Semester 5)
Electromagnetic Fields and Waves
December 2015
Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

Attempt any four of the following:-
1(a) Find the charge enclosed in a cube of having side of 2 m with the edges of the cube parallel to axes x, y and z while origin is at the centre of the cube. The charge density within the cube is 50x2 $\cos\left ( \dfrac{\pi}{2}y \right )$ μC/m3.
5 M
1(b) Explain the concept of potential gradient and the relation between electric field and potential.
5 M
1(c) If the magnetic field H =(3x cos β+6z sin α) $\hat{a}$ y. Find the current density ȷ if field are invariant with time.
5 M
1(d) Discuss the phenomenon of polarization in dielectric medium. Also discuss how it gives rise to bond charge densities.
5 M
1(e) For a lossy dielectric material having μr=1,εr and σ=20 s/m. Calculate the propagation constant at a frequency of 16 Ghz.
5 M

2(a) Given D 2rz cos2 φ $\hat{a}$r -rz sin φ cos φ [\hat{a}\]φ+r^2Cos2φ a z. Calculate electric flux through the following surfaces.
(i) r=3, 0≤z≤5. (ii) z=0, 0≤r≤3.
10 M
2(b) Obtain E inside, outside solid sphere, A uniform volume charge density ρv c/m3, Distributed in a solid sphere of radius 'a' find expression of E everywhere.
10 M

3(a) Planes z=0 and z=4 carry a current K =-10 $\hat{a}$x A/m and K =10 $\hat{a}$x A/m respectively. Find H at points (i) P(1, 1, 1) and (ii) Q(0, -3, 10)
10 M
3(b) Obtain an expression for magnetic vector potential in the region surrounding infinitely long straight filamentary current 'I'
10 M

4(a) Derive the Poission's and Laplace equation. And the one dimensional laplace's equation is as $\dfrac{\partial^2 y}{\partial x^2}$ =0, The boundary conditions are V = 9 at X = 1 and V = 0 at X = 10. Find the potential and show the variation of V with respect to X.
10 M

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