This question was asked in IIT JEE 2010. I know that the electrostatic pressure is equal to (1/2)∈(E)² and if we multiply this with the projected area then we would get the force acting on an object holding charge. In the solutions of this question the electric field is taken to be (σ/ϵ) as the electric field on the surface of any one of the hemispherical conductors is (σ/ϵ) and then the total force acting on the other hemispherical shell is found out by multiplying that electrostatic pressure with the projected area , i.e. , (π*(r)^2). But I do not understand that why the electric field is taken to be (σ/ϵ) . Though the electric field due to any conductor on it's surface is equal to (σ/ϵ), it is not constant throughout the surface of the other hemispherical shell. Therefore , the electrostatic pressure should not be constant throughout the surface of any one of the shells.
So , how can we use this formula for finding the electric force on the complete body?
σ - Charge density of the hemispherical shells; ϵ - permittivity of free space; E - Electric field