Q. No. 1
(a) Apply Gauss’s law to find out the electric field at an arbitrary point near a thin insulating sheet of infinite extent having a uniform charge density σ. 10
(b) What are the limitations of Coulomb’s law? 03
(c) Two point charges, -q and (½)q, are situated at the origin and at the point (a,0,0), respectively. At what point along the x-axis does the electric field vanish? 07

Q. No. 2
(a) State and prove the uniqueness theorem. 10
(b) Explain why foods that contain water can be cooked in a microwave oven. 03
(c) Two spherical conducting shells of radii r_a and r_b are arranged concentrically and are charged to potentials φ_a and φ_b, respectively. If r_a > r_b, find the potential at points between the shells and at points r > r_a. 07

Q. No. 3
(a) What is magnetic vector potential? Give its physical significance. Derive an expression for the magnetic vector potential in terms of current density. 10
(b) Use the concept of magnetic pole density and surface density of magnetic pole strength to explain why the poles of a uniformly magnetized bar magnet lie at its ends. 03
(c) The magnetic moment of a macroscopic body is defined as ∫_V M dv. Prove the relationship: ∫_V M dv = ∫_V r ρ_M dv + ∮_S r σ_M da where S is the surface bounding V. 07

Q. No. 4
(a) Draw a circuit diagram for a N-P-N transistor in common emitter configuration. Explain how it works as a voltage amplifier. What modification is needed to convert it into an oscillator? 10
(b) Explain how diode works as a rectifier. 03
(c) What are semiconductors? Explain how doping leads to the fabrication of N-type and P-type semiconductors. 07

Q. No. 5
(a) Draw a circuit diagram to demonstrate the use of a triode as a receiver. Explain how it works. 10