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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.

[itex]\lambda=\frac{∂q}{∂l}[/itex]

[itex]\oint E \bullet \Delta A = \frac{\sum q}{\epsilon}[/itex]

He then jumps to.

[itex]E \int \Delta A = \frac{\lambda L}{\epsilon}[/itex]

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

[itex]E \int \Delta A[/itex] 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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# Surface integral to Lateral integral?

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