Hi. I have this problem, and when I tried to solve it, some doubts and questions emerged, I need some help with this. The problem says:(adsbygoogle = window.adsbygoogle || []).push({});

The figure shows two concentric cylindrical conductors with infinite length. We'll suppose that between them there's a known potential difference.

a. Find an expression for the family of equipotential surfaces for the interior of the configuration.

b. Get the expressions for the density surface charge in each cylinder.

Fig. 1

Well, I tried to get the electric field, and then the expression for the potential. I think that what I did is actually wrong. I considered a charge Q distributed over the inner surface. Then considered the surface charge distribution.

[tex]\frac{Q}{2\pi l a}=\sigma \rightarrow Q=\sigma l 2\pi a[/tex]

Gauss:

[tex]E 2\pi r l=\frac{\sigma l 2\pi a}{\epsilon_0}[/tex]

[tex]E=\frac{\sigma a}{\epsilon_0 r}\vec{r}[/tex]

[tex]V(r)=-\int_a^r E \dot dr=-\frac{\sigma a}{\epsilon_0} \int_a^r \frac{dr}{r}=-\frac{\sigma a}{\epsilon_0} \ln \left (\frac{r}{a} \right), a<r<b[/tex]

The doubts that emerged were with respect to if it was necessary to consider the charge to get the difference in the potential between the cylinders. And in the other hand if I shouldn't consider an other field due to the induced surface charge over the cylinder at radii b (its a conductor, so there should be an induced image charge on it).

Thanks for your help in advance :)

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# Homework Help: Electrostatics, infinite concentric cylindric conductors

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