The problem is: Consider a parallel-plate capacitor with plates of area A and with separation d. Find F(V), the magnitude of the force each plate experiences due to the other plate as a function of V, the potential drop across the capacitor. Express your answer in terms of given quantities and [tex]\epsilon_0[/tex].(adsbygoogle = window.adsbygoogle || []).push({});

2. The equation I figured I needed to use for this was one for the potential energy stored in a capacitor. [tex]U_c=\frac{\epsilon_0}{2}(Ad)E^2, E=\frac{\Delta V}{d}[/tex]

Well, I figured that because force is the derivative of potential energy, I could just take the derivative of the potential energy equation and get what I needed:

[tex] \frac{d}{dV}(\frac{\epsilon_0}{2}(Ad)(\frac{\Delta V}{d})^2)[/tex]. From this I get [tex]\frac{\epsilon_0 AV}{d}[/tex], having done the proper substitution for E in terms of my given variables (A,d, and V.) I am using "Masteringphysics" is anyone is familiar with that. I also attempted another means, by which I used the formula F=EQ, and substituted [tex]E=\frac{Q}{\epsilon_0 A}[/tex] and [tex]Q=\frac{\epsilon_0 A}{d}*\Delta V_C[/tex]

After doing this, the answer I got was [tex]\frac{V^2 \epsilon_0 A}{d^2}[/tex]. Apparently I am off by some "multiplicative factor" (I hate it when the program tells me this...) but I haven't the damndest clue as to what it is.

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# Homework Help: Parallel Plate Capacitor Force

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