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8B-Soln05-v1.0.1 - 8B Worksheet Answers 5 Capacitance 1 a C...

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8B Worksheet Answers 5. Capacitance 1. a) C = ε 0 A / d b) V C = V c) Q = CV = ε 0 AV / d d) U = CV 2 / 2 = ε 0 AV 2 / 2 d e) The plate separateion, d increases, and A and Q are held fixed. Q is 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, C decreases by a factor of 3, Q stays the same, V C = Q / C increases by a factor of 3. For U we have to be careful - we can’t just take d and make it 3 d , since the d came from the expression for the charge, which is now fixed. Therefore, we will take U = Q 2 / 2 C as our expression. Q is fixed, and C decreases, so U increases by a factor of 3. f) The increase in stored energy U comes 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 away from each other, and this
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