#### Dielectrics, polarization; Solutions to boundary-value problems-conducting and dielectric spheres in a uniform electric field;

Questions:

**Q 1.** A region 1, $z<0$, has a dielectric material with $\epsilon_r=3.2$ and a region 2, $z>0$ has a dielectric material with $\epsilon_r=2.0$. Let the displacement vector in the region 1 be, $\vec D_1 = -30a_x+50a_y+70a_z nCm^{-2}$. Assume the interface charge density is zero. Find in the region 2, the $\vec D_2$ and $\vec P_2$, where $\vec P_2$ is the electric poliarization vector in the region 2. **[20 marks]**

**Q 2.** Two charged spheres of radius R each, have their centres a distance d apart such that d < 2R. One of the spheres has a uniform positive charge density $\rho$ per unit volume while the other has opposite charge density – $\rho$ . Show that the electric field in the region of overlap between two spheres is uniform. **[15 marks]**

Video Solution at 11 pm