(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two parallel plates with area A and charges Q and -Q are being pulled apart by force F, so that the distance between, x, slowly increases. Express F in terms of Q, A and x.

2. Relevant equations

[tex]-\Delta PE=W[/tex]

[tex]W=\int Fdx[/tex]

[tex]\Delta PE=q_{0}\Delta V[/tex]

[tex]Q=C\Delta V[/tex]

[tex]C=\frac{A\epsilon_{0}}{d}[/tex]

3. The attempt at a solution

[tex]Q=C\Delta V[/tex]

[tex]Q=\frac{A\epsilon_{0}}{x}\Delta V[/tex]

[tex]\Delta V=\frac{Qx}{A\epsilon_{0}}[/tex]

[tex]q_{0}\Delta V=\Delta PE[/tex] and in this case q_{0}= -Q

[tex]\Delta PE=\frac{Qx}{A\epsilon_{0}} (-Q)[/tex]

[tex]W=-\Delta PE=-\frac{-QQx}{A\epsilon_{0}}[/tex]

[tex]W=\frac{Q^{2}x}{A\epsilon_{0}}[/tex]

[tex]W=\frac{Q^{2}x}{A\epsilon_{0}}=\int Fdx[/tex]

Force is then equal to the derivative of my expression with respect to x.

[tex]F=\frac{Q^{2}}{A\epsilon_{0}}[/tex]

How can I get an answer independent of x? It.. just doesn't make sense to me. My friend and I both got this answer independently. Where have we gone wrong, or is it correct or.. something? I'm rather confused.

(Ohhh the pain, did you know that Ctrl+W closes a tab [at least in Firefox]? Yeah, I was going to write W and managed to hit Ctrl instead of Shift.. towards the end of my attempt at a solution.)

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# Homework Help: Parallel plates and force

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