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Introductory Physics Homework Help
2 Capacitors and energy density
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[QUOTE="Steve4Physics, post: 6825125, member: 681522"] Yes. All the arguments are now correct (and give the same conclusion!). You might consider slightly more detail. For example for 1) you could note: a) volume ##\propto A##; b) ##E \propto \frac 1A##; c) so ##U \propto A(\frac 1{A^2}) \propto \frac 1A##. Doing the maths along with the qualitative analyse is very useful. For example, you may be able to understand (qualitatively) that some quantity Y decreases when quantity X increases, but without the proper analysis you won’t know the precise relationship, e.g. is ##Y \propto \frac 1X## or is ##Y \propto \frac 1{X^2}## or something else?. To derive the equation for ##U## in terms of ##\epsilon , A, d## and ##Q## is straightforward. The dependence of ##U## on ##A## (for fixed ##Q## and ##d##) will then be very clear. By the way, another intuition into the problem is to note that to put a charge onto a small area requires more work than putting the same onto a larger area – because of the additional work needed to overcome the mutual repulsion between the charge-elements. [/QUOTE]
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Introductory Physics Homework Help
2 Capacitors and energy density
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