A very very long hollow cylinder has inner radius a outer radius b it has a known uniform charge per unit volume p. Find the difference in the electric potential between a point on the axis and a point a distance a+d from the axis of the cylinder where a+d

Respuesta :

According to Gauss Law:

[tex]\phi=E.A=\frac{q_{enclosed}}{\epsilon_o}[/tex]

By Gauss's law, at R = A+D

[tex]E(2\pi R l) =\frac{\rho \pi R^2 l}{\epsilon_o}+\frac{\rho \pi A^2 l}{\epsilon_o}\\E=\frac{\rho}{2\epsilon_o}(R+\frac{A^2}{R})[/tex]

Potential is given as

[tex]V=\int\limits^{A+d}_A {E} \, .dR=\frac{\rho}{2\epsilon_o}[(\frac{R^2}{2})^{A+D}_A-A^2lnR^{A+D}_A]\\V=\frac{\rho}{2\epsilon_o}[\frac{(A+D)^2}{2}-\frac{A^2}{2}-A^2ln\frac{A+D}{A}][/tex]