Calculating Electrostatic Pressure on a Charged Metallic Sphere

[zargle]

Homework Statement

We are told to consider a thin uniform metallic sphere carrying a charge Q. First we found the electrostatic energy of the electric field E and now we are told to find the electrostatic pressure on the sphere from this.

Homework Equations

The Attempt at a Solution

We are told not to use the sigma^2 /2*epsilon_0 formula.

For my energy I got Q^2/(8pi*epsilon*R). How do I turn this into a electrostatic pressure? Do I go about it using the diagonal elements of the maxwell stress tensor?

Sorry for lack of more work, but I am COMPLETELY jammed up on this and don't really have more than this. I just need a point in the right direction to get me moving on this.

Thanks

 

[Jhero]

for your question! It sounds like you are on the right track by considering the Maxwell stress tensor. The diagonal elements of the stress tensor can be used to calculate the electrostatic pressure on the sphere. Specifically, the pressure can be calculated as P = (1/2)(E^2 + B^2) - (1/2)epsilon_0E^2, where E is the electric field and B is the magnetic field. Since we are dealing with an electrostatic situation, the magnetic field is zero, so the equation simplifies to P = (1/2)epsilon_0E^2. From here, you can substitute in your expression for the electric field (which I assume is Q/(4pi*epsilon_0*R^2)) and solve for the pressure. I hope this helps! Let me know if you have any further questions.