[UPSC CSE 2009] Electrostatics and Magnetostatics (Q177, 10M)

A thin dielectric cylindrical rod of cross-section A is situated along z-axis from z = 0 to z = L. The polarisation of the rod is along its length and it is given by \vec{P} = (2z^2 + 5)\hat{z}. Calculate bound volume charge density at each end of the rod.