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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,
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