DAY 3 – DAW February

 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