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Calculating equivalent capacitance.

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A parallel plate capacitor of capacitance $C$ without dielectrics is filled by a dielectric slab as shown here, the new capacitance will be?

When I solve it in two ways as shown here I got different results as $3.9C$ and $4C$ respectively, why? And which one is correct, please help.

asked Apr 9 in Physics Problems by n3 (508 points)
retagged Apr 12 by sammy gerbil

1 Answer

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Best answer

The middle diagram shows the correct equivalent configuration.

The diagram on the right assumes that the potential is the same at all points of the interface between the upper and lower dielectrics. If this is true then the interface can indeed be replaced by a conducting plate and the upper dielectric becomes a single capacitor, as suggested in the right-hand diagram.

However, the interface is a dielectric surface not a conducting surface, so it need not be at the same potential at all points adjacent to each of the two lower dielectrics. The lower surface of the upper dielectric can be split into two surfaces which can be at different potentials. This is recognised in the middle diagram.

answered Apr 12 by sammy gerbil (28,448 points)
edited Apr 13 by sammy gerbil
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