BHP301Sample Examination Paper — I

Section A — Short Answer (Compulsory)

1. State Gauss's law in electrostatics and write its integral form. (2 marks)
2. Define electric displacement D and state its relation to E and P. (2 marks)
3. State the Biot–Savart law. (2 marks)
4. Distinguish between diamagnetic and paramagnetic materials. (2 marks)
5. State Lenz's law and explain its physical significance. (2 marks)
6. Define power factor of an AC circuit. (2 marks)
7. Write Maxwell's equations in integral form (any two). (2 marks)

Section B — Attempt any two parts of each

1. Using Gauss's law, derive the electric field due to an infinitely long charged cylindrical conductor. (5 marks)
2. Derive the boundary conditions on D and E at the interface between two dielectric media. (5 marks)
3. Using Ampere's circuital law, derive the magnetic field inside a long solenoid. (5 marks)
4. Derive an expression for the impedance and resonant frequency of a series RLC circuit. (5 marks)
5. State and prove Thevenin's theorem with a suitable circuit example. (5 marks)

Section C — Attempt any two questions in full

1. State and derive Gauss's law from Coulomb's law, and use it to find the electric field due to (i) an infinite charged plane sheet and (ii) a uniformly charged solid sphere, both inside and outside. (10 marks)
2. Derive Laplace's and Poisson's equations for electrostatic potential and explain the Uniqueness theorem. Discuss the potential and field of an electric dipole. (10 marks)
3. Derive the magnetic field due to a straight current-carrying conductor and a circular current loop using the Biot–Savart law, and discuss the torque experienced by a magnetic dipole in a uniform field. (10 marks)
4. Derive expressions for self and mutual inductance for a pair of coaxial solenoids, and discuss the energy stored in an inductor carrying steady current. (10 marks)
5. Explain Maxwell's modification of Ampere's law through the concept of displacement current. Write Maxwell's equations in both integral and differential form and show how they predict electromagnetic waves travelling at the speed of light. (10 marks)