Solution

Past exam of the mathematics course of the University of Cambridge / 2007 / ib / Paper 3 / 17E / Solution

Past exam of the mathematics course of the University of Cambridge / 2009 / ib / Paper 3 / 17A / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 2 / 4D / Solution

For coaxial cylinders of radii $a<b$ and length $L\gg b$, carrying charges per unit length $\pm\lambda$,
$$
E(r)=\frac{\lambda}{2\pi\epsilon_0r}\widehat r,
\qquad
V=\frac{\lambda}{2\pi\epsilon_0}\log\frac ba,
\qquad
C=\frac{2\pi\epsilon_0L}{\log(b/a)}.
$$
The field energy is $U=\lambda^2L\log(b/a)/(4\pi\epsilon_0)=QV/2$.

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 Incoming links: Coaxial cylindrical capacitor