8B Worksheet Answers 5. Capacitance 1. a) C= ε0A/ db) VC= Vc) Q= CV = ε0AV/ dd) U= CV2/ 2 = ε0AV2/ 2de) The plate separateion, dincreases, and Aand Qare held fixed. Qis held fixed, rather than V, because the plates are no longer connected to the battery, or to anything else, so the net charge on one of the plates can’t move to the other plate. Therefore, Cdecreases by a factor of 3, Qstays the same, VC= Q/ Cincreases by a factor of 3. For Uwe have to be careful - we can’t just take dand make it 3d, since the dcame from the expression for the charge, which is now fixed. Therefore, we will take U= Q2/ 2Cas our expression. Qis fixed, and Cdecreases, so Uincreases by a factor of 3. f) The increase in stored energy Ucomes from the fact that we have to add energy into the system to move the plates away from each other. That is, the plates are oppositely charged and thus feel an attractive force towards each other. We have to do work on the system to move the charged plates awayfrom each other, and this
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