Gauss's Law: Charge Distribution in Cylinder Volume

Click For Summary
SUMMARY

This discussion focuses on applying Gauss's Law to a uniformly charged infinite cylinder. The first part demonstrates that the electric field E at a distance r from the cylinder (where r < R) is given by E = (ρ * r) / (2ε°), where ρ is the volume charge density. The second part of the problem requires deriving the expression for E when r > R, prompting further clarification on the variables involved in the application of Gauss's Law.

PREREQUISITES
  • Understanding of Gauss's Law and its applications
  • Familiarity with electric field concepts
  • Knowledge of volume charge density (ρ)
  • Basic calculus for manipulating equations
NEXT STEPS
  • Research the derivation of electric fields for different charge distributions
  • Study the application of Gauss's Law in cylindrical symmetry
  • Learn about the behavior of electric fields outside charged conductors
  • Explore advanced topics in electrostatics, such as potential energy in electric fields
USEFUL FOR

Students studying electromagnetism, physics educators, and anyone preparing for exams involving electrostatics and Gauss's Law applications.

Toyona10
Messages
31
Reaction score
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


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

Similar threads

  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 16 ·
Replies
16
Views
3K
  • · Replies 7 ·
Replies
7
Views
6K
Replies
1
Views
3K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 8 ·
Replies
8
Views
12K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
5
Views
2K
Replies
4
Views
2K
Replies
9
Views
2K