The dielectric cylinder is radius R and thickness d. Origin is at the center of the cylinder, which is oriented along the z-axis. It has polarization P=pz∧I need to calculate the potential V(0,0,h) at h>d/2.
The Attempt at a Solution
I've actually done a lot of work to reach the equation above. In example problems, such as with a sphere, σ ends up with a cosφ term that can be used to set their coefficients equal to each other and solve for the An and Bn terms. In this problem, however, the normal unit vector n∧ is parallel with the direction of polarization so σ=p. Since σ has no sin or cos terms, I can't solve for An and Bn. What am I supposed to do, or more likely, what did I do wrong?