Physics 230 Capacitor exercise with dielectrics




Question: How do we get the biggest capacitance if we have enough dielectric to fill half of the capacitor volume? (It is a parallel plate capacitor.)




The two main choices look like this:

capdiel__1.png capdiel__2.png

In the first case the capacitor may be modelled as two capacitors in series. The individual capacitances are:
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Thus the total capacitance is given by:
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and thus
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In the second case our model is two capacitors in parallel. The individual capacitances are
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So the total capacitance is
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To find which is the biggest we must compare $C_{s}$ and $C_{\Vert }.$ Is
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Equivalently, is
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Yes! Thus the capacitor on the right has the greatest capacitance.

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