Section A
Q1.
(a)
(i) Obtain the partial differential equation governing the equations f(u, v) = 0, u = x + yz, v = x + y + z
(ii) Construct a partial differential equation of all surfaces of revolution having z-axis as the axis of rotation.
(b) Discuss the phenomena of Hysteresis in ferromagnetic materials. On the B-H curve show the retentivity, coercivity and saturation points. What is coercive force and the energy dissipated per unit volume of the ferromagnetic substance during the hysteresis cycle?
(c) Explain and derive continuity of current equation using the principle of conservation of charge.
(d) Using the principle of superposition, determine the current I in the 5 \Omega resistor in the circuit shown in the figure. 1 - 5Ω ≶ 20 \Omega 30 V ξ 10 \Omega 6A 15~Omega
(e) State Ampere's circuital law. A hollow conducting cylinder has inner radius a and outer radius b and carries current I along the positive z-direction. Find H everywhere.