Electromagnetics -- parallel plate capacitor energy storage

timeforplanb

1. The problem statement, all variables and given/known data
A parallel-plate capacitor 0.5m by 1.0m has a separation distance of 2cm and a voltage difference of 10V. Find the stored energy, assuming that ε=εo. If a 200-volt potential is applied in the capacitor, (a) determine the energy stored; (b) hold d1 at 2cm and the voltage difference at 200V, while increasing d2 to 2.2cm, determine the final stored energy.

2. Relevant equations
U=(1/2)(CV²)
C=εS/d


3. The attempt at a solution
(a)
C=((8.854x10^-12)(0.5x1.0))/(0.02)
C=2.2135x10^-10 F

U=(1/2)(2.2135x10^-10)((10+200)²)
U=4.8808x10^-6 J

(b)
C=((8.854x10^-12)(0.5x1.0))/(0.022)
C=2.0123x10^-10 F

U=(1/2)(2.0123x10^-10)((10+200)²)
U=4.4371x10^-6 J

I'm not sure what to do with the voltage difference of the capacitor, so I added it with the voltage potential applied.

BruceW

Yeah, I'm not sure what it means by the voltage difference of the capacitor and the applied potential. I would guess that they are two separate questions, i.e. work out the answer with 10V, then also work out the answer with 200V (in other words, don't add them together).

And for part b, what does d1 and d2 mean? Are they the positions of the two plates, or are they the positions of one of the plates in two different situations?

jegues

d1 and d2 is the distance between the two plates of the capacitor.

timeforplanb

So I saw my classmate's answer for this problem and for (b), d in C=ε_oS/d is d=(d₁+d₂)/2? Why is this so?

BruceW

That still doesn't help my confusion. I'm not sure if d2-d1 is the separation of the plates, or if d2 is the separation of the plates. (because they start with a separation of 2cm, then d2 is increased to 2.2cm, so this seems like the separation is d2).

BruceW

This would suggest that the separation between the plates is (d1+d2)/2 Which is odd. Do you have a picture of the set-up?

timeforplanb

The thing is, our professor didn't give us an illustration or anything. One of my classmates just drew the set-up - two plates separated by d and that's it.

Sir, can I post another question here and my solution to it? It's about electromagnetics too.

BruceW

If it's another question, you will probably get more replies by making a new thread for it. But you can post it here too if you'd like. About this question, I guess you are meant to use (d1+d2)/2 for the separation, and I would guess to use 200V, but it might be different depending on what your classmate had in mind. Anyway, It looks like you get the idea of how to do the calculation, but you were just unsure on the specific set-up in this case.

jegues

The way I understood it was like so,

In part (a) find the stored energy for a voltage of 200V, and a distance d1 inbetween the plates.

In part (b) find the stored energy for a voltage of 200V, and a distance d2 inbetween the plates.