I asked the following question to my teacher through email a week ago, and he hasn't replied. Consider a uniformly charged spherical shell of radius R and areal density [itex]\sigma[/itex] and consider also a cartesian system whose origin coincide with the center of the shell. Clearly if we attempt to calculate the field at r = R directly through Coulomb's law, we obtain that the field is undefined, because we'd have a (r' - r') at the denominator (equ. 2.7 in Griffiths) But, as Griffiths remarks (pp.88), if we apply Gauss' Law, we obtain that the field at r = R is of magnitude [itex]\sigma \epsilon_0[/itex]. So what should we think? Is the sclalar function E(r) undefined at r = R or not ?!