DAY 3 – DAW February

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


Q 1. A region 1, z<0z<0, has a dielectric material with ϵr=3.2\epsilon_r=3.2 and a region 2, z>0z>0 has a dielectric material with ϵr=2.0\epsilon_r=2.0. Let the displacement vector in the region 1 be, D1=30ax+50ay+70aznCm2\vec D_1 = -30a_x+50a_y+70a_z nCm^{-2}. Assume the interface charge density is zero. Find in the region 2, the D2\vec D_2 and P2\vec P_2, where P2\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 ρ\rho  per unit volume while the other has opposite charge density – ρ\rho  . Show that the electric field in the region of overlap between two spheres is uniform. [15 marks]

Video Solution at 11 pm