#### Laplace and Poisson equations in electrostatics and their applications; Energy of a system of charges, multiple expansion of scalar potential

Questions:

**Q 1.** Starting from the Laplace’s equation in a cylindrical polar coordinate system and using the method of separation of variables , obtain the differential equations for the solution of r, $\theta$ and z component of the potential. ** [15 marks]**

**Q 2.** A 0.5m long cylindrical medium between two conducting plates has a uniform charge density of $100 nC/m^3$.The axial of the cylindrical medium is along the z-axis. The left plate is at $z=0$ and has a potential of $10kV$ and the right plate is grounded. Determine the electric field at axial distance $z=0.2m$. **[15 marks]**

Video Solution at 11 pm