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Electric Capacitance, Energy of an Electric Field

Problem 3.141

Each plate of a parallel-plate air capacitor has an area SS. What amount of work has to be performed to slowly increase the distance between the plates from x1x_{1} to x2x_{2} if (a) the capacitance of the capacitor, which is equal to q,q, or (b) the voltage across the capacitor, which is equal to V,V, is kept constant in the process?

Reveal Answer
3.141. (a) A=q2(x2−x1)/2ε0SA=q^{2}\left(x_{2}-x_{1}\right) / 2 \varepsilon_{0} S (b) A=ε0SV2(x2−x1)/2x1x2A=\varepsilon_{0} S V^{2}\left(x_{2}-x_{1}\right) / 2 x_{1} x_{2}
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