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Potential Between Different Dielectric

For the last question I posted, the Key says the answer is 0.50 nF.
How do they get that answer?

P.S. I have Teflon being 2.1 and paper being 3.5

Since the potential between point a and b is the potential between the plates, when a capacitor is half filled with a different dielectric, then we can describe the system as two capacitors linked in a parallel. Both "new" capacitors have half the original plate area.

The first capacitor C1 is filled with air (air=1), while the other capacitor C2 is filled with paper (paper=1)

Therefore, the capacitors values are:

Since these capacitors are linked in parallel the total capacitance is the sum of the two capacitors.
Hence:

All is left now is to plug in the numbers, making sure all the units agree:

Thus:

Therefore:

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Since the potential between point a and b is the potential between the plates, when a capacitor is half filled with a different ...

Solution Summary

The potentials between the different dielectrics are determined. A system of two capacitors are provided.

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