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#### Quintessential

##### New member

- Feb 3, 2014

- 7

I feel that although I "know of" these topics, I don't actually "flow with them".

Ignoring the math for a second; I want to form an understanding. And I think calculating the capacitance formula of a cylindrical capacitor may help.

*****From that picture I understand that the center cylinder has a positive value, and the outer cylinder has an equal and opposite value.

*****There must be an electric field in midst of the cylinders flowing from the positive to the negative.

*****(

*I'm still confused with the electric potential portion, but here goes*) There is also an electric potential tied together with this field. And to find this potential \(\displaystyle V\), I must find the Electric Field \(\displaystyle E\).

*****I know: \(\displaystyle \oint_S {E_n dA = \frac{1}{{\varepsilon _0 }}} Q_{inside}\)

*****Using the given gaussian surface on that picture, I should find \(\displaystyle E\).

*****Once I find \(\displaystyle E\), I should plug it into the formula: \(\displaystyle \Delta V=-Ed\) and \(\displaystyle d\) being the distance \(\displaystyle (b-a)\). Because, (

*...not certain*) the electric field multiplied by a given distance equals the electric potential for that given distance.

*****Now that I have \(\displaystyle \Delta V\) I use the following: \(\displaystyle C=\frac{Q}{\Delta V}\). I know the electric potential and the charge is \(\displaystyle Q\). With that, I find the capacitance.

I haven't done any calculations to prove this. I only wanted to know if my intuition was legal.

Thank You.