Question
Consider a parallel plate capacitor with metal plates, each of square shape of 1.00 m on a side, separated by 1.00 mm. What is the internal energy stored in this system if the charge on the capacitor is 30.0 μC?
Final Answer
Solution video
OpenStax College Physics for AP® Courses, Chapter 19, Problem 42 (Test Prep for AP® Courses)
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Video Transcript
This is College Physics Answers with Shaun Dychko. A parallel plate capacitor with a side length of 1.00 meter— the plates are square by the way— these are separated by 1.00 millimeter, which is 1.00 times 10 to the minus 3 meters and each plate has a charge of 30.0 microcoulombs, which is 30.0 times 10 to the minus 6 coulombs, the question is how much energy is stored in this capacitor? So energy is going to be the charge squared divided by 2 times the capacitance and we have a formula for the capacitance in terms of the area of each plate and their separation d. This formula requires multiplying area divided by separation by the permittivity of the material between the plates and since we are told nothing about any material between the plates, we'll have to assume that it is air, which essentially has a permittivity of free space close enough that we can just use this ε naught for our permittivity. The area of each plate is the side length squared. So we take this formula here, substitute for C so we are dividing by this fraction and instead of dividing a fraction by this fraction, I am going to multiply by the reciprocal of this fraction so I am going to multiply by d over ε naughtl squared. So the energy stored then is the charge squared times the separation between plates divided by 2 times permittivity of free space times the side length of each plate squared and that is 5.08 times 10 to the minus 2 joules.