Consider a long teflon rod (a dielectric cylinder) with radius a oriented along the z-axis. imagine that we could set up a permanent polarization p(s, theta, z) = ks vector, where s is the usual cylindrical radial vector from the z-axis. and k is a constant). the cylinder is sufficiently long that you can neglect end effects.

a. calculate sigma b and row
b. what are the units of your constant k? use these hound charges along with gauss's law to find the e vector inside and outside the cylinder.
c. find the electric displacement field (d vector) inside and outside the cylinder using griffiths eqn. 4.21 and verify that griffiths eqn. 4.23 works out. explain briefly in words.