So far I have learned about Coulomb's law, the electric field, gauss's law, the electric potential and now capacitance.

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.