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## Homework Statement

Calculate the electric field of a cylindrical capacitor comprised of a smaller cylindrical conductor of radius ##a## enclosed within a larger cylindrical conductor of radius ##b## where ##b>a##. The smaller cylinder has charge ##+Q## and the larger cylinder has charge ##-Q##.

## Homework Equations

$$\oint \vec{\mathbf{E}} \cdot \vec{\mathbf{dA}} = \frac{Q_{\text{enclosed}}}{\epsilon_0}$$

## The Attempt at a Solution

I've already solved the problem, as follows:

Define a Gaussian surface in which the cylinder completely encloses the smaller cylinder and is completely within the larger cylinder, i.e. a Gaussian cylinder with radius ##r## where ##a<r<b##.

Furthermore, let ##L## denote the length of the cylinder.

$$(2 \pi r L) E = \frac{Q_{\text{enclosed}}}{\epsilon_0}$$

$$E = \frac{Q}{2 \pi r L \epsilon_0}$$

While this is trivially easy, this reference sheet assumes that ##L >> b## prior to calculating anything.

Why must this be done?

Thank you,

Eigenvaluable