A parallel plate capacitor with plate area A = 100 cm^2 and plate separation of d = 5mm is connected to a 120 Volt power supply and allowed to fully charge.
a) Calculate the capacitance, stored charge, electric field midway between the plates and potential energy stored.
The capacitor is disconnected from the power supply and then a sheet of glass of thickness b = 2mm with dielectric constant κ = 4.5 in place between midway between plates.
b) Calculate the electric field inside the dielectric and in the gaps between the dielectric and the capacitor plates.
c) Hence calculate the voltage across the plates, and thus the new capacitance.
d) Calculate the new stored energy and determine whether work was done or given out as the glass plate was inserted.
C = ε0A/d
Q = CV
E = Q/ε0A
u = (1/2)CV^2
The Attempt at a Solution
I've been trying my luck at this question. So for part a) I obtained all that was asked for without taking recourse to integrals. It seemed too easy to be the correct method to go about the problem. I simply substituted what was given in the question into the formulas noted above, and then substituted the resultant quantities into other equations to get the remaining quantities asked for. I also said that the direction of the electric field is perpendicular to the capacitor plates, from positive to negative.
As for part b) where the dielectric is taken into account, I obtained the electric field strength inside the dielectric by simply considering that it would be the field strength E without the dielectric divided by the dielectric constant k. The direction of it being the same as in the case where there is no dielectric.
However I'm not sure on how to go about calculating the electric field between the dielectric and the capacitor plates?
And for the following parts, is it still simply a case of substituting the known values into the above equations to get the desired quantities?