C = Q V ( C o l V o l t = F a r a d a y ) = σ A V = σ d / ϵ ∵ V = E d = σ d ϵ {\displaystyle C={\frac {Q}{V}}{\begin{matrix}{\begin{smallmatrix}(\end{smallmatrix}}{\frac {Col}{Volt}}{\begin{smallmatrix}=\,Faraday\,)\end{smallmatrix}}\end{matrix}}={\frac {\sigma A}{V=\sigma d/\epsilon }}\quad \because V=Ed={\frac {\sigma d}{\epsilon }}}
a b {\displaystyle a\;b}
V = ∫ a b k Q r 2 d r = − k Q [ 1 r ] a b = k Q ( 1 a − 1 b ) C = Q V = 1 k a b b − a {\displaystyle {\begin{aligned}&V=\int _{a}^{b}{\frac {kQ}{r^{2}}}dr=-kQ\left[{\frac {1}{r}}\right]_{a}^{b}=kQ\left({\frac {1}{a}}-{\frac {1}{b}}\right)\\&C={\frac {Q}{V}}={\frac {1}{k}}{\frac {ab}{b-a}}\end{aligned}}}
![{\displaystyle {\begin{aligned}&V=-\int Edr=-\int {2k\lambda }rdr=-2k\lambda \int {\frac {1}{r}}dr=-2k\lambda \ln r\\&V=\int _{a}^{b}{\frac {2k\lambda }{r}}dr=2k\lambda {\Big [}\ln r{\Big ]}_{a}^{b}=2k\lambda \ln {\frac {b}{a}}\\&C={\frac {Q}{V}}={\frac {l}{2k\ln {\frac {b}{a}}}}\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2cc83c2b17d5b39483844026050c75e6441c29a2)
![{\displaystyle {\begin{aligned}&V=\int _{a}^{b}{\frac {kQ}{r^{2}}}dr=-kQ\left[{\frac {1}{r}}\right]_{a}^{b}=kQ\left({\frac {1}{a}}-{\frac {1}{b}}\right)\\&C={\frac {Q}{V}}={\frac {1}{k}}{\frac {ab}{b-a}}\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d5ca2c24b2b87da8d07a42ba88f10766dc37b037)
