Not sure if this is advanced. Highly doubt it but oh well(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Consider an infinitely long charged cylinder of radius R, carrying a charge whose density varies with radius as ρ(r) = ρo r. Derive expressions for the electric field (a) inside the cylinder (i.e. r<R), and (b) outside the cylinder (i.e. r>R).

2. Relevant equations

Gauss's Law

q=ρ δτ

3. The attempt at a solution

(a) E inside cylinder

I sketched a Gaussian surface inside of the cylinder.

I believe that E is parallel to ds ( E⃗ ||ds⃗ )

So, gauss's law becomes E∮ds = q/ϵ for the side

I believe the integral of ds is 2π r L (L being the length of the cylinder even though it is infinite.

And q = ρo r π r2 L

derived from q=ρ δτ

So we have E (2π r L) = ρo r π r2 L /ϵ

Simplifying to E = ρo r2/ 2ϵ

Is this correct for (a)?

And for (b) would it be the same idea but with a gaussian surface outside of R?

Thanks!

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# Homework Help: Electromagnetism: Gauss's Law

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