The figure below shows a circular hole of radius b (white) bored through a spherical shell (gray) with radius R and uniform charge per unit area σ.

(a) Show that E(P) = (σ/2ε₀)[1 − sin(θ₀/2)]ˆr, where P is the point at the center of the hole and θ₀ is the opening angle of a cone whose apex is at the center of the sphere and whose open end coincides with the edge of the hole. Perform the calculation by summing the vector electric fields produced at P by all the other points of the shell.

(b) Use an entirely different argument to explain why E(P) ≈ (σ/2ε₀)ˆr when θ₀

| 2R- 2b T