• Support PF! Buy your school textbooks, materials and every day products Here!

Gauss Law

  • #1

Homework Statement


I am to find the electric field for a charge distribution of
$$ \rho(x)= e^{-\kappa \sqrt{x^2}} $$


Homework Equations



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

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?
 

Answers and Replies

  • #2
56
2
Is [itex] x [/itex] a vector? If not, assume one dimension. Your surface area will most likely be of a sphere. Also, recall that [itex] q_{enc} [/itex] is the total charge. Can you think of another (more formal) way to write [itex] q_{enc} [/itex]?
 
  • #3
[itex] x [/itex] 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 [itex] q_{enc} [/itex] can be written as [itex]\int \rho(x)[/itex] I believe. So I should be able to just integrate my charge distribution from [itex] -x [/itex] to [itex] x [/itex] and consider the area a sphere of radius [itex]x[/itex]? 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:
  • #4
56
2
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
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
56
2
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?
 

Related Threads on Gauss Law

  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
2
Views
882
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
20
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
11
Views
936
Top