Question

5. (20 points) For many dielectric materials, the relationship between the displacement field D and the electric field E in the material is linear and can be represented simply by th equation D-eE, where ε is the permittivity of the medium. Consider now two long, co- axial cylindrical conducting shells separated by such a dielectric (see the cross-sectional figure below). Let the surface charge density on the inner cylinder with radius a be +o, and assume that the charge is uniformly distributed over the surface of the cylinder. (a) Find the magnitude and direction of the displacement field D in the region between the two cylindrical shells. Hint: Use Gauss' law for dielectrics. (b) Find the magnitude and direction of the polarization field P in the region between the cylinders (c) Compute the volume density of bound charge in the dielectric. (d) Compute the surface density of bound charge on the physical surfaces of the dielectric. (e) Verify directly that the total bound charge in the system is zero.

Answer 1

iven hot dlisplacemen Piald d The euatio ti. Radius Given diaqsam irelos in shape ause ss ao 2>

$2 Ca CCA 9n RADIALy OUTUDARD

6 a usig ouss laus, ウ cvetestat) Bauin on C- CL

LS ata

9n a. crt a Total bcund che

コ0-9TTkh +9.TT kh Total bond Charge Θ6-c