A spherical shell of radius R is divided into three conducting segments by two very thin air gaps located at latitudes 0 and

A spherical shell of radius R is divided into three conducting segments by two very thin air gaps located at latitudes θ₀ and π − θ₀. The center segment is grounded. The upper and lower segments are maintained at potentials V and −V , respectively. Find the angle θ₀ such that the electric field inside the shell is as nearly constant as possible near the center of the sphere.