1. Show that the potential at a point distant r1 and r2 respectively from the centres of a long parallel pair of wires of negligible cross-section are having equal and opposite linear charge density A. coulombs per metre, is given by
<img src='./qimages/10893-1.jpg'>
2. Derive the capacitance of a cylindrical coaxial capacitor using Laplace equation.

3. Calculate the induced dipole moment per unit volume of helium gas placed in an electric field of 6 x 10^5 V/m. The molecular polarisability of helium is 2·33 x 10^-41 Farad-m^2 and the density of helium is 20.6 x 10^25 molecules/m^3.

4. State Biot-Savart law and relate it to Ampere's law. Show that the divergence of magnetic induction is always zero.

5. Show that the equation of continuity div J dp/dt 0 is contained in Maxwell's equations.

6. Deduce an expression for the velocity of propagation of a plane electromagnetic wave in a medium of dielectric constant e and permeability
M

7. Calculate the degree of polarisation for ordinary light reflected from glass (refractive index 1.5) at an angle of incidence 45°.

8. Show that the energy of interaction between two balls, whose distribution of charges e1 and e2 is
spherically symmetric, equals to <img src='./qimages/10893-8.jpg'> where the distance between the centres of the balls is a.

9. Show that the potential function

$ q y^2

satisfies the Laplace's equations.

10. Write short notes on any two of the following:
Impedance Matching
Boundary Conditions in Electrostatics
Standing Waves