Lectures 10 problems (Displacement Field, Boundary Conditions for E & D, Revisit

Gauss' Law)

10.1. Consider a pair of concentric spherical conductors. The inner sphere is of radius a and

contains a uniformly-distributed charge Q; the larger sphere is grounded and of inner radius c.

The space between the conductors is filled with two non-conducting, charge-free dielectrics, of

permittivity &1 (a

displacement field D in the space between the conductors. (b) Find the electric field E in the two

dielectric media. (c) Determine the potential difference Vo between the conductors. (d)

Determine the surface charge densities ps on the surfaces of the conductors.

10.2. Consider the plane interface between two perfect dielectric media defined by y = -2x. The

relative permittivity for y< -2x is &1 =2, while for y> -2x it is &2=3. The displacement field D

for medium 1 at the boundary is D₁ = 4ax - 6ay (C/m²). Determine the displacement field D₂ in

1

medium 2 at the boundary. Find the angle ai between Di and the surface normal and the angle

a₂ between D2 and the surface normal.

10.3. Consider the plane interface between a perfect conductor (y <-2x) and a dielectric medium

with permittivity & = 480 (y> -2x). A surface charge density in the surface of the conductor is ps

= -2 nC/m². Determine D, E, and P in the two media close to the interface. Use P in the

dielectric to determine the effective surface charge density Ps,eff-