# Gauss' Law

## 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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Gyroscope

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Thats what it sayss....

Gyroscope
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 $$E=\frac{\lambda}{2\pi \epsilon_0 r}$$, cant 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 dont really understand this stuff.