IGNOU BPHCT-133 - Electricity and Magnetism

PART A 1. a) Determine the direction in which the scalar field f(x, y) = 2x 2 y 2 + xy increases most rapidly at the point (1, 1). b) Calculate the work done by a force in moving a particle once counter-clockwise along the ellipse c) Use the divergence theorem to calculate the flux of a vector field over a cube of side 2a which has its vertices at 2. a) Consider the figure given below. Charges q1, q2 and q3 are placed at P, Q and R, respectively, and q1 = q2 = -q3 = 2μC. Determine the magnitude and the direction of the electric field at point A. b) Determine the electric field of a uniformly charged infinite solid cylinder of radius R at a point (i) outside the cylinder, and (ii) inside the cylinder. c) Obtain an expression for electric potential due to an electric dipole at an off axis point at a distance r from the midpoint of the dipole. PART B 3. a) The separation between the plates of a parallel plate capacitor is 3 mm and the cross-sectional area of the plates is 5.5 x 10–4 m –2. A dielectric material of dielectric constant 5.0 is filled between the plates of the capacitor and a voltage of 80 V is applied across the plates. Calculate (i) the capacitance of the capacitor, (ii) charge stored on each plate, (iii) displacement D, and (iv) polarization P. b) Explain the concept of current density and derive continuity equation. What form does the continuity equation takes for steady currents? c) A toroid has 500 turns and it carries a current of 8 A. Calculate the magnetic field within the toroid at a point which is at a distance of 15 cm from its centre. 4. a) A typical ignition coil made up of two coils draws a current of 4.0 A and supplies an emf of 25 kV to the spark plugs. If the current in the two coils is interrupted every 0.15 ms, calculate their mutual inductance. b) Explain the physical significance of the Maxwell’s equation Derive the wave equation for the electric field of an electromagnetic wave. c) Consider an electromagnetic wave in vacuum whose electric field is given by Determine the direction of propagation, the wave number, the frequency and the magnetic field of the wave.