Gauss's Law: Charge Distribution in Cylinder Volume

In summary, the conversation discusses the uniform distribution of charge in an infinitely long cylinder and the resulting electric field at various distances from the cylinder. It is shown that at a distance r from the cylinder (where r<R), the electric field is given by E= (ρ*r)/2ε°, where ρ is the volume charge density. The conversation also mentions using Gauss' law to determine the electric field at distances greater than the cylinder's radius.
  • #1
Toyona10
31
0

Homework Statement


Charge is distributed uniformly throughout the volume of an infinitely long cylinder of radius R.
a)Show that at a distance r from the cylinder (r<R): E= (ρ*r)/2ε° where ρ is the volume charge density and (b) write and for E when r>R


Homework Equations





The Attempt at a Solution


hey guys...i was able to prove the first part:
as q= ρv= ρ∏r^2 * L

EA= Q/ε

E= (ρ∏r^2L)/ε°2∏rL >> after cancelling i got that expression in the question...

and about the b part, do we just do the same thing...which r do we substitute? Please help asap

 
Physics news on Phys.org
  • #2


It's the same old Gauss law! EA = q/e0 as you say.
What are q and A now?
 

What is Gauss's Law?

Gauss's Law is a fundamental law in electromagnetism that relates the electric flux through a closed surface to the charge enclosed by that surface. It is a mathematical statement of the fact that electric charges create an electric field.

How is Gauss's Law related to charge distribution in a cylinder?

Gauss's Law can be used to calculate the electric field at any point inside or outside of a charged cylinder. By using a Gaussian surface in the shape of a cylinder, the electric flux through the surface can be related to the charge enclosed within the cylinder.

What is the formula for Gauss's Law in a cylinder volume?

The formula for Gauss's Law in a cylinder volume is:

∮E•dA = Qenclosed0

where ∮E•dA is the electric flux through a closed cylindrical surface, Qenclosed is the charge enclosed by the surface, and ε0 is the permittivity of free space.

How can Gauss's Law be used to find the electric field inside a charged cylinder?

By using a Gaussian cylinder as the closed surface in Gauss's Law, the electric field inside the cylinder can be calculated by rearranging the formula to solve for E. This can be useful in understanding the behavior of electric fields and charges within a cylinder.

What are some applications of Gauss's Law in cylinder volume?

Gauss's Law can be applied in various practical situations, such as determining the electric field inside a charged capacitor, analyzing the behavior of charged particles in a particle accelerator, and understanding the behavior of plasma in a fusion reactor. It is also an important tool in the study of electric fields and charges in general.

Similar threads

  • Advanced Physics Homework Help
Replies
16
Views
2K
  • Advanced Physics Homework Help
Replies
7
Views
4K
  • Advanced Physics Homework Help
Replies
2
Views
2K
  • Advanced Physics Homework Help
Replies
8
Views
7K
  • Advanced Physics Homework Help
Replies
1
Views
932
  • Advanced Physics Homework Help
Replies
1
Views
3K
  • Advanced Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Advanced Physics Homework Help
Replies
9
Views
2K
  • Advanced Physics Homework Help
Replies
4
Views
1K
Back
Top