Calculating Required Surface Charge Density for a Cylinder

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In summary, the problem involves a long straight wire with a linear charge density of 3.6nC/m that is enclosed by a thin, non-conducting cylinder with a positive surface charge density \sigma. The goal is to find the required \sigma value that will result in a net external electric field of zero. This can be done by applying Gauss's Law and using a gaussian surface, such as another cylinder, and setting the condition that the integral of the electric field over the surface is equal to zero. By solving for \sigma in the equation E=\frac{\sigma}{\epsilon_0}, the required value can be found.

Homework Statement

A long, straight wire has a linear charge density of magnitude 3.6nC/m. The wire is to be enclosed by a thin, no-conducting cylinder of ouside radius 1.5cm, coaxil witht he wire. The cylinder is to have positive charge on its outside surface with a surface charge density $$\sigma$$ such that the net external electric field is zero. Calculate the required $$\sigma$$.

Homework Equations

$$E=\frac{\lambda}{2\pi \epsilon_0 r}$$

The Attempt at a Solution

The electric field can be found, but then how do I go about finding the required $$\sigma$$ value?

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Thats what it sayss...

The wire has obviously negative charge. Hasn't it?
Apply Gauss's Law, to a gaussian surface, I recommend you to use another cylinder, and put the condition that:

$$\oint E\cdot dS=0$$

Im still confused

The total field is zero right? It is due to a superposition of the field from the wire and the field from the cylindrical shell.

So Do I just find an electric field for the gaussian surface that when summed with the electric field already found wll equal zero?

not sure what exactly you mean there

Since the total electrical field is 0, and I can find $$E=\frac{\lambda}{2\pi \epsilon_0 r}$$, can't I just find $$E=\frac{\sigma}{\epsilon_0}$$

and then $$\frac{\lambda}{2\pi \epsilon_0 r} = -\frac{\sigma}{\epsilon_0}$$ and then solve for $$\sigma$$

Sorry if this make no sense, I don't really understand this stuff.