Answer to Question #290955 in Electricity and Magnetism for Shah

Question

Find the total charge of a cylinder of Radius R and Length L, carrying a charge density that is proportional to the distance from its axis.

Answer 1

$\oint\vec Ed\vec A=\frac q{\varepsilon_0},$

$E(2\pi r)L=\frac{\rho \pi r^2L}{\varepsilon_0},$

$E=\frac{\rho r}{2\varepsilon_0}.$