A cylinder (bottom face at z = -L, top face at z = L, radius R, centered along the z-axis) carries a volume charge distribution ΓΒ(ΓΒ, Γβ , z) = ΓΒo (z/L) cos^2Γβ .
a. Calculate the monopole and dipole moments of this charge distribution.
b. Find the leading order terms for the potential and the electric field at the point (x = 25R, y = 25R, z = 25L).