7) Suppose the entire region below the xy plane (z ≤ 0) is filled with a uniform (homogeneous, isotopic)

linear dielectric material of susceptibility Xe. A uniform line charge X is placed on an infinite straight wire,

a distance d above the xy plane and parallel to the x axis.

a) Express the bound surface charge ob in terms of the electric field at the boundary, just inside the

dielectric, E.

b) Find the relevant component(s) of the electric field from the line charge at a point just inside the

dielectric.

c) Find the electric field from the bound surface charge ob at the same point (just inside the dielectric.)

d) Use the above to solve for the surface charge Ob. (Hint: substitute your expressions for the electric

field from parts (b) and (c) into your expression for σ, from part (a).)

e) Find the total charge per unit length in the x direction on the surface and compare your result to the

surface charge induced in an infinite conducting plane by an infinite uniform line charge density (see

problem 3.10).

f) Use the comparison from part (e) to choose a reasonable bound charge densities and positions to

use as image charges, and write an expressions for the resulting potentials above and below the xy

plane. Clearly specify and explain the reasonig behind the image charge placement in both cases.

g) Show that -Eo (@Vabove/oz | 2-0-OV below /dz|2=0) = Ob from part (d).