1.78 Hole in a shell **
Figure 1.52 shows a spherical shell of charge, of radius a and sur- face density σ , from which a small circular piece of radius b « a has been removed. What is the direction and magnitude of the field at the midpoint of the aperture? There are two ways to get the answer. You can integrate over the remaining charge distribution
to sum the contributions of all elements to the field at the point in question. Or, remembering the superposition principle, you can think about the effect of replacing the piece removed, which itself is practically a little disk. Note the connection of this result with our discussion of the force on a surface charge – perhaps that is a third way in which you might arrive at the answer.