R = ∫ d R = ∫ σ d r a = ∫ σ d r 2 π r L = σ 2 π r L ∫ b a d r r = σ 2 π r L ln b a {\displaystyle {\begin{aligned}&R=\int dR=\int {\frac {\sigma dr}{a}}=\int {\frac {\sigma dr}{2\pi rL}}\\&={\frac {\sigma }{2\pi rL}}\int _{b}^{a}{\frac {dr}{r}}={\frac {\sigma }{2\pi rL}}\ln {\frac {b}{a}}\end{aligned}}}