## Self Assessment Quiz

1. Find the first few multipole moments of a linear quadrupole aligned along the x direction and also when it is aligned along y direction.

2. Three linear quadrupoles are arranged along the x, y and z axes with the central charge of each being at the origin and the  other two charges  at a distance a each from the origin. Show that the quadrupole moment of this superposition of the quadrupoles is zero. What is the lowest non-vanishing multipole of this configuration?

3. A rectangular parallelepiped having dimension filled with a dielectric in which the polarization is given by , where is the position vector  of a point in the dielectric with respect to the centre of the parallelepiped. Find the bound charge densities in the dielectric and show that the total bound charge is zero.

4. A line charge with a linear charge density λ is in the vacuum, at a distance d from the surface of a semi-infinite dielectric of permittivity ε . Obtain the  image charge that must be put at a distance d inside the dielectric to simulate the charge density at the boundary when the entire space  has  permittivity .

5. At the interface between two dielectrics with relative permittivity 2 and 3, there is a free charge density C/m2. The electric field strength in the first medium has a magnitude V/m and its direction makes an angle of with the interface.  Find the electric field in the second medium.