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Electric field in the hole on surface of a sphere

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A large conducting spherical shell of radius a, and fixed surface charge density (sigma), has a small circular hole in the surface of radius b<<a. [Note the cap of radius b is measured on the curved surface, not the chord, so that the angle subtended, alpha, at the center of the sphere from the center of the hole to the edge of hole alpha = b/a]

Use direct integration over the surface of the sphere to find the electric field in the hole at its center and show what happens in the limit as b-> infinity.

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Problem has been solved using integration.

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