1(a)
State Gauss theorem of electrostatics. List characteristics of Gaussian surface.

5 M

1(b)
Determine electric flux density 'D' in Cartesian coordinates caused at p(6, 8, -10) by i) a point charge of 30 mc at origin ii) infinite line charge with ρ

_{r}= 40 μc/m ii) A surface charge with ρ_{s}= 57.2 μc/m^{2}on a plane z = -9m.
8 M

1(c)
Evaluate both side of divergence theorem for the region r ≤ a (spherical coordinates) having flux density \( D=\dfrac{5r}{3}a_r\ c/m^2\)

7 M

2(a)
Prove that : E = -∇V

5 M

2(b)
Determine work done in carrying a charge of -2C from (2, 1, -1) to (8, 2, -1) in an electric field E = ya

_{x}+ xa_{y}v/m along the path x = 2y^{2}.
7 M

2(c)
Three point charges 3 coul, 4 coul and 5 coul are to be situated at corner of an equilateral triangle of side 5 m. Find energy density at the centre of triangle.

8 M

3(a)
Derive Poisson's and Laplace equation.

6 M

3(b)
A potential field given by v = x

^{2}yz + Ay^{3}z volts determine of 'A' such that v satisfies Laplace equation and hence find electric field E at p(2, 1, -1).
6 M

3(c)
A spherical capacitor has a capacitance of 54 pF. It consists of two concentric spheres with inner and outer radii differing by 4 cm. Dielectric in between is air. Determine inner and outer radii.

8 M

4(a)
State and explain Ampere's circuital law.

5 M

4(b)
Determine magnetic flux density 'B' at 'P' for a current loop shown in Fig. Q4(b).

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9 M

4(c)
Clearly distinguish between scalar magnetic potential and vector magnetic potential.

6 M

5(a)
Derive Lorentz force equation for a moving change placed in a combined electric and magnetic field.

6 M

5(b)
A point charge Q = 18 nc moves with a velocity of 5 × 10

^{6}m/sec in the direction of 0.06a_{x}+ 0.75a_{y}+ 0.3a_{z}. Determine magnitude of force experienced by the charge when placed in i) electric field E = -3a_{x}+ 4a_{y}+ 6a_{z}kv/m ii) magnetic field E = -3a_{x}+ 4a_{y}+ 6a_{z}mT iii) combined E and B.
8 M

5(c)
An air cored toroid has a cross sectional area of 6 cm

^{2}, a mean radius of 15 cm and is wound with 500 turns and carries a current of 4A. Find the magnetic field intensity at the mean radius.
6 M

6(a)
Explain Faraday's ;aws applied to : i) stationary path, changing field ii) steady field, moving circuit.

6 M

6(b)
List Maxwell's equations for both : i) steady and ii) Time varying fields in differential and integral form, also mention the relevant laws they demonstrate.

8 M

6(c)
A straight conductor of length 0.2m, lies on x-axis with one end at origin. The conductor is subjected to a magnetic flux density B = 0.04a

_{y}Tesla and the velocity v = 2.5 sin 10^{3}ta_{z}m/sec. Determine motional emf induced in the conductor.
6 M

7(a)
Derive wave equation for E in a general medium.

6 M

7(b)
State and explain Poynting theorem.

6 M

7(c)
A lossless dielectric medium has σ = 0, &mu

_{r}= 1, ε_{r}= 1. A electromagnetic wave has field as H = -0.1 cos (ωt - z)a_{x}+ 0.5 sin (ωt - z)a_{y}A/m. Find : i) phase constant, ii) angular velocity iii) the wave impedance iv) components of electric field intensity of the wave.
8 M

8(a)
Derive an expression for transmission coefficient and reflection coefficient and relate them.

8 M

8(b)
Define standing wave ratio. Write an expression for it.

4 M

8(c)
Determine the amplitude of reflected and transmitted 'E' and 'H' at the interface between two regions. Characteristics of region 1 are ε

_{η}= 8, μ_{r1}= 0; &sigma_{1}= 0 and region 2 is free space. The incident E_{0}^{1}in region 1 is of 1.5 V/m. Assume normal incidence. Also find average power in two regions.
8 M

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