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Figure 1.52 shows a spherical shell of charge, of radius
a and surface 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? Solve this exercise using direct integration.
Electric field at the center of integrated charged sphere is zero so when we remove the disc shaped portion, there will develop an electric field at the center of remaining aperture which will be equal in magnitude to the electric field of the disc at its axis at a distance equal to radius of sphere and opposite in direction.
Charge density = 
, radius of disc = b, distance over the axis = R.
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