Question

Plaese help!

Suppose you have an infinite non-conducting cylinder of charge of radius R, and uniform charge density lambda. Starting from Gauss' Law, show: that the Electric Field inside is given by: E = lambda r/2 pi epsilon_o R^2 the Electric Field outside is given by E = lambda/2 pi epsilon_o r A big part of your grade will depend on how accurate and detailed your picture is, and how clean and clear your resulting derivation is.

Answer 1

consider a long cylinder of radius R and uniform charge density $\lambda$ let us find the electric field at a distance r from the axis cylinder

consider a cylindrical gaussian srface of length L and radius r

basing on electric flux

$\int E.ds=Qenclosed/\epsilon$

$Qenclosed =\lambda r L$

$E[2\pi R*L]=\lambda rL/\epsilon R$

$E=\lambda r/2 \pi \epsilon R^2$

[b] ans

basing on gauss law

$\int E.ds=Qenclosed/\epsilon$

$Qenclosed =\lambda L$

$E[2\pi rL]=\lambda L/\epsilon$

$E=\lambda /2\pi \epsilon r$

hence the therom is proved