1. a) Define divergence and curl of a vector field and determine divergence and curl of following vectors. i) F = x^2y^3 + z^2i, ii) F = sin(2θ)φ + p^2zθ + 2z cos(θ), iii) F = x^2z... 1. a) Define divergence and curl of a vector field and determine divergence and curl of following vectors. i) F = x^2y^3 + z^2i, ii) F = sin(2θ)φ + p^2zθ + 2z cos(θ), iii) F = x^2z + y^2i. 2. a) Write Laplace's and Poisson's equations and derive expressions of electric field intensity and potential due to double charge. b) Derive equation of continuity and find energy of a system of three charges - 1nC, 4C and 3nC located at (0, 0, 0), (0, 2, 0) and (1, 0, 0) respectively. 3. a) Write Biot Savart's law and derive expression of magnetic field intensity due to straight current carrying conductor. b) Derive magnetic boundary conditions and calculate total magnetic flux crossing the surface. 4. a) Write Faraday's law and explain transformer and motional emf in detail. b) Discuss following in brief: i) Scalar and vector potential, ii) Self and mutual inductance, iii) Maxwell’s equations for static and time varying fields, iv) Energy stored in magnetic field. 5. a) A uniform plane wave in a medium has E = 2e^{-α}sin[10^4 - βz] A/m. If the medium is characterized by ε_r = 20 and σ = 3 S/m, find α and β. b) Write pointing vector theorem and discuss reflection of plane wave for normal and oblique incidence. 6. a) State Gauss Law and determine the total charge enclosed by the cylinder of radius 1m with -2 ≤ z ≤ 2m. Given that electric flux density D = 2ρcos(2θ) A/m². b) Write boundary value conditions for electric field and discuss capacitances for various types of capacitors. 7. a) A lossy dielectric has an intrinsic impedance of 200-30jΩ at a particular radian frequency ω. If at that frequency the plane wave propagating through the dielectric has the magnetic field component H = 10e^{-α}cos(rac{z}{2}) A/m. Find E and H and determine skin depth. b) Derive wave equation in dielectrics and discuss polarization of waves. Read more