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AKG

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**Problem**: A metal sphere of radius

*R*carries a total charge

*Q*. What is the force of repulsion between the "northern" hemisphere and the "southern" hemisphere?

My book gives a formula for the electrostatic pressure:

[tex]P = \frac{\sigma ^2}{2\epsilon _0}[/tex]

pushing the surface outwards (and hence pushing the northern hemisphere away from the southern one). I can find [itex]\sigma[/itex]:

[tex]\sigma = \frac{Q}{4\pi R^2}[/tex]

so I get:

[tex]P = \frac{Q^2}{32\pi ^2 \epsilon _0 R^4}[/tex]

The force acting on one hemisphere will be the pressure times the area of that hemisphere, which is just [itex]2\pi \R^2[/itex], so I get:

[tex]F = \frac{Q^2}{16\pi \epsilon _0 R^2}[/tex]

Is this right? The whole problem seems weird to begin with, I'm not sure if the numbers I'm using actually give me the quantity I'm looking for, and not just some other quantity related to the system. So is this right? Thanks.