Solve Charge Density (rod) Homework Problem

Click For Summary
SUMMARY

The discussion centers on solving a charge density problem involving a rod with a nonuniform linear charge density defined as λ = ax, where 'a' is a positive constant. Participants utilize the electric potential formula V = kq/r and the integral form of electric potential to derive the solution. The challenge lies in correctly applying the limits of integration and understanding the relationship between the variables involved, particularly how to handle the variable 'x' in the context of the integral.

PREREQUISITES
  • Understanding of electric potential and electric field equations (V = kq/r, E = kqq/r²).
  • Familiarity with calculus, specifically integration techniques.
  • Knowledge of charge density concepts, particularly nonuniform charge distributions.
  • Ability to interpret and manipulate mathematical expressions involving limits of integration.
NEXT STEPS
  • Study the derivation of electric potential for nonuniform charge distributions.
  • Learn about the application of integration in electrostatics, focusing on charge density problems.
  • Explore the relationship between total charge Q and linear charge density λ for various configurations.
  • Investigate the use of the integral form of electric potential in different coordinate systems.
USEFUL FOR

Students in physics or engineering courses, particularly those focusing on electromagnetism, as well as educators seeking to clarify concepts related to charge density and electric potential calculations.

jesuslovesu
Messages
185
Reaction score
0
Never mind, i got it, whew

Homework Statement


http://img137.imageshack.us/img137/6250/chargqg0.th.jpg
The rod has a nonuniform charge density lambda = ax (a is a positive constant). Find electric potential at point A.

Homework Equations


V = kq/r
E = kqq/r^2
V = -\[ \int_a^b E dot dr\]

The Attempt at a Solution


I am pretty close to the answer, I'm just not quite there.
If I'm not mistaken it is something like:
\[ \int_d^{L+d} kax*r/r^2\,dr
but I'm not quite sure what to do with the 'x', from the answer, I know that it has to end up being the integral of 1/r, so x can't be r because it would end up being just the integral of dr

Maybe the limits are incorrect?
 
Last edited by a moderator:
Physics news on Phys.org
Hi! I have a similar problem...

A rod of length L lies along the y-axis with its center at the origin. The rod has a nonuniform linear charge density lambda =a | y | , where a is a constant with the units {\rm C}/{\rm m}^{2} . Determine the constant a in terms of L and the rod's total charge Q.

I know that for uniform charge its lambda=L*Q and then integrate but what do I do in this case?

Thanks!
 

Similar threads

Replies
11
Views
1K
Replies
6
Views
3K
Replies
3
Views
2K
Replies
4
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
3
Views
3K
  • · Replies 18 ·
Replies
18
Views
5K
  • · Replies 5 ·
Replies
5
Views
4K