# Gauss Law

1. Sep 17, 2013

### rodriguez1gv

1. The problem statement, all variables and given/known data
I am to find the electric field for a charge distribution of
$$\rho(x)= e^{-\kappa \sqrt{x^2}}$$

2. Relevant equations

I know that gauss law is $$\int E \cdot da = \frac{q_{enc}}{\epsilon_0}$$

3. The attempt at a solution

I am not sure what the charge distribution looks like. Is this saying that there is only charge along the x axis? or is the charge everywhere? I am also no sure what kind of surface I should be integrating over. Should I be integrating over a circle and then finding the total charge enclosed within?

2. Sep 17, 2013

### Bryson

Is $x$ a vector? If not, assume one dimension. Your surface area will most likely be of a sphere. Also, recall that $q_{enc}$ is the total charge. Can you think of another (more formal) way to write $q_{enc}$?

3. Sep 17, 2013

### rodriguez1gv

$x$ appears to be a scalar. Does this mean that the charge only exists along the x axis? Or is it also distributed through the y-z plane? And the $q_{enc}$ can be written as $\int \rho(x)$ I believe. So I should be able to just integrate my charge distribution from $-x$ to $x$ and consider the area a sphere of radius $x$? That doesn't seem quite right to me for some reason since I have an x symmetry should I be using a cylinder? similar to a line of charge along the x axis?

Last edited: Sep 17, 2013
4. Sep 17, 2013

### Bryson

Yes, really what we have is a point charge in one dimension, where we only consider the charge density along the x-axis. I suppose a cylinder would be fitting for Gauss's Law. Yes, you are correct about integrating along the x-axis.

5. Sep 17, 2013

### rodriguez1gv

Using a cylinder seems to give me a dependence on both x and y. I feel like there should be a simpler choice of surface, but I cannot seem to think of it. I have also tried a sphere centered at the origin. I am not sure how I would apply a plane.

6. Sep 17, 2013

### Bryson

Perhaps, we can treat this similar to the case for an infinite wire? Are we finding the E-field at some point say on the y-axis, or some point on the x-axis?

Must we use Gauss's Law?