 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

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 ρr = 40 μc/m ii) A surface charge with ρs = 57.2 μc/m2 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 = yax + xay v/m along the path x = 2y2.
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 = x2yz + Ay3z 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).
:!mage
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 × 106 m/sec in the direction of 0.06ax + 0.75ay + 0.3az. Determine magnitude of force experienced by the charge when placed in i) electric field E = -3ax + 4ay + 6az kv/m ii) magnetic field E = -3ax + 4ay + 6az mT iii) combined E and B.
8 M
5(c) An air cored toroid has a cross sectional area of 6 cm2, 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 = 0.04ay Tesla and the velocity v = 2.5 sin 103 taz 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, &mur = 1, εr = 1. A electromagnetic wave has field as H = -0.1 cos (ωt - z)ax + 0.5 sin (ωt - z)ay 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 εη = 8, μr1 = 0; &sigma1 = 0 and region 2 is free space. The incident E01 in region 1 is of 1.5 V/m. Assume normal incidence. Also find average power in two regions.
8 M

More question papers from Field Theory