Pressure on charged spherical shell, alternative solution

[Pifagor]

Homework Statement

Find the pressure on a uniformly charged spherical conducting shell of Radius R and total charge Q. The answer is (Q^2) / (32*π*ε*R^4)

I´m fine doing this using the derivative of the energy as the sphere grows to get the force.

My question is: Why do I get twice the answer if I think of a small surface element dA and calculate the force on it as the field E = Q/(4πεR^2) multiplied by the charge on that surface element, dQ = dA*(Q/(4πR^2) ?

I cannot see where I double the force. How should this approach be mended?

Thanks for reading this,

Pifagor

 

[Nate810]

Homework Equations Electric field due to a uniformly charged spherical shell: E = Q/(4πεR^2)The Attempt at a Solution This approach should work, as the field due to a uniformly charged spherical shell is given by E = Q/(4πεR^2). Thus, if we consider a small surface element dA, the force on it will be F = dQ*E = dA*(Q/(4πR^2))*(Q/(4πεR^2)) = (Q^2)/(32πεR^4). This is twice the correct answer. I believe this has to do with the fact that, in this approach, I am considering the force on one side of the spherical shell, while the correct answer considers the force on both sides of the shell. Thus, in order to get the correct answer, we must divide our result by two. This gives us the correct answer of (Q^2) / (32*π*ε*R^4).