What is the Electric Field of an Infinite Line of Charge?

[Void123]

Homework Statement

Pretty much, I am given an infinite line of charge and asked to find the electric field (using Gauss' theorem) at some arbitrary position $$r^{\vec{}}$$.

Homework Equations

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The Attempt at a Solution

I don't think its that confusing, except for the part with the position vector. I am assuming I just model the line as a 'cylinder' and insert its associated area for da in the surface integral. Correct? But, would I just put in the magnitude of the position for $$r$$ when computing the area? Or is it a bit more complicated?

 

[Gokul43201]

The line should be treated as a line, not a cylinder. The area involved in Gauss' theorem is not that of the object containing the charge, but of something else. You will know what this "something else" is when you carefully read the statement of the theorem.

You should follow the steps involved in solving any standard problem using Gauss' theorem. What is the first step in this process?

 

[Void123]

Gauss' Theorem states that the flux through any surface with a charge distribution is equal to the total charge within that surface times some constant.

But what surface am I talking about if I am only working with a line?

Also, then, how come examples solving electric fields for an infinite line of charge use the cylinder method?