1. The problem statement, all variables and given/known data A thick-walled cylindrical tube of dielectric material has internal radius a/2 and external radius 2a, and its polarization is given in cylindrical coordinates by the expression P = (A/r2) er. Derive expressions for the net charge on the inner and outer surfaces of a length L of the tube and for the charge within the volume of length L of the tube. 2. Relevant equations σb = P . n hat where n hat is the outward-pointing unit vector normal to the surface and P is the polarization. surface area of cylinder (ignoring ends) = 2∏rL 3. The attempt at a solution σb total = σb inner + σb outer σb outer = (A/(2a)2) * area of cylinder σb outer = (A/(2a)2) * 2∏(2a)L σb outer = ∏AL/a Now the bit I can't seem to marry with the model answer . . . σb inner = (A/(a/2)2) * 2∏(a)L σb inner = (4A/a2) * 2∏(a)L σb inner = 8∏AL/a At least that's how I got it. The model answer shows it to be σb inner = 4∏AL/a It has to be a problem I'm having with algebra again, but I can't see where. Could you show me where I went wrong please. Or am I right?