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

Archived Gauss Law and the wrong Gaussian surface.

  • Thread starter Scherejg
  • Start date
5
0
1. Homework Statement

The problem was to calculate the electric field inside an infinite length cylinder (with radius R) with a non uniform charge density. The charge density depended on r. Its easy enough to solve using a gaussian cylinder with r less than R. But what if I wanted to complicate things and use a gaussian sphere inside the cylinder with r < R?

2. Homework Equations

∫E[itex]\bullet[/itex]dA = q / ε° Gauss' Law

ρ = ρ°(1 - r/R) This is charge density distribution

q = ρ[itex]\bullet[/itex]dV

V= 4/3 π r^3

A= 4 π r^2

3. The Attempt at a Solution

Since the electric field is not the same everywhere, it can't be removed from the first integral. It is however constant over dθ when r and d[itex]\Phi[/itex] are held constant.
q =∫ ρ*dV = ∫ ρ°(1- r/R) * A* dr
q = ∫ρ°(1-r/R) * 4 π r^2 * dr
q is easy enough to solve. So the problem lies in ∫E*dA
I had a few ideas about this, First one: convert the problem into spherical coordinates and solve it that way. Second one: The electric field is a vector quantity, so could I say the total electric field at a point r is equal to the sum of the partial derivatives of the electric field at that point? In that case, I would need to find an expression for dE/d[itex]\Phi[/itex]. Any guidance on this would be appreciated. Thanks!
1. Homework Statement



2. Homework Equations



3. The Attempt at a Solution
 
As I understand r is the distance from axis, so you can not find the total enclosed charge inside a sphere by simply integrating ρ = ρ°(1 - r/R) you first need to convert r to spherical coordinates. After doing that you can try to solve equations for electric field but probably it will not be easy because taking a sphere as gaussian surface actually makes thing worse than finding electric field using Poisson's equation.
 

Want to reply to this thread?

"Gauss Law and the wrong Gaussian surface." You must log in or register to reply here.

Related Threads for: Gauss Law and the wrong Gaussian surface.

Replies
3
Views
487
Replies
1
Views
882
  • Posted
Replies
7
Views
12K
  • Posted
Replies
4
Views
4K
  • Posted
Replies
1
Views
5K
  • Posted
Replies
16
Views
5K
Replies
2
Views
1K
  • Posted
Replies
2
Views
3K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top