1. The problem statement, all variables and given/known data Find the electrostatic force of interaction between two halves of a spherical conductor of radius R carrying a charge Q. This thread already exists- https://www.physicsforums.com/threads/electric-force-between-two-halves-of-a-sphere.317380/ but is closed. 2. Relevant equations Electrostatic pressure: dF/dA = σ2/2ε0 3. The attempt at a solution I understand how to do it using the method outlined in the above mentioned thread, but I want to do it using the argument stated in the last post of the thread, the one that mentions this at the very end: "By the way, I think the "supposed way" to do this Griffith problem is to use the formula for surface pressure of a conductor earlier in the chapter and add up the integrate z-component of the force on the base and the side of a hemisphere. Be ware, you need to make a correct physical argument about the direction of the pressure/force." So, to solve it, I tried splitting up the northern hemisphere as elementary rings. Basically, here's what I'm trying to do: Take an elementary area dA containing a charge dq on an elementary ring of radius r. The force acting on dq is dF = ( σ2 dA ) / 2ε0 Now comes my problem- I'm not sure what the net force on the ring should be, should it be ∫dFsinθ or ∫dFcosθ, i.e. should I take the vertical components or the horizontal components? So, I tried using both and got the right answer using ∫dFsinθ Here's what I did: The net force on the ring is F (ring) = ∫dFsinθ = ∫( σ2 2πRcosθRdθ sinθ) / 2ε0 and F(hemisphere) = ∫F(ring) Integrating from 0 to π/2 I get Q2 / 32πεR , which is correct. But I still don't get why I'm choosing ∫dFsinθ over ∫dFcosθ.