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Plaese help! Suppose you have an infinite non-conducting cylinder of charge of radius R, and uniform...

Question

Plaese help! Suppose you have an infinite non-conducting cylinder of charge of radius R, and uniform...
Plaese help!

Suppose you have an infinite non-conducting cylind
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.

Answers

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


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