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## Surface integral to Lateral integral?

1. The problem statement, all variables and given/known data
I have some working out my lecture gave me to a problem and I don't think I understand part of it. Hoping you could help me.

It's using Gauss' Law to find the capacitance of a cylindrical capacitor of length L but this information shouldn't matter for my question.

$\lambda=\frac{∂q}{∂l}$

$\oint E \bullet \Delta A = \frac{\sum q}{\epsilon}$

He then jumps to.

$E \int \Delta A = \frac{\lambda L}{\epsilon}$

First question, how does he go from the surface integral to the normal integral? Has it got anything to do with removing the dot product?

He then changes
$E \int \Delta A$ to E(2πrL)

I understand this is taking the integral of dA which becomes A, which is the area of a circle, hence 2πr, but how does he then bring the L into play...would this not be the Volume, not the area?

Thanks for any help.
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