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 50x

^{2}\[\cos\left ( \dfrac{\pi}{2}y \right )\] μC/m^{3}.
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 μ

_{r}=1,ε_{r}and σ=20 s/m. Calculate the propagation constant at a frequency of 16 Ghz.
5 M

2(a)
Given D 2rz cos

(i) r=3, 0≤z≤5. (ii) z=0, 0≤r≤3.

^{2}φ \[\hat{a}\]_{r}-rz sin φ cos φ [\hat{a}\]_{φ}+r^2Cos^{2}φ 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 ρ

_{v}c/m^{3}, 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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