Finding magnitude of x-component Electric Field due to a Line Charge

Click For Summary

Homework Help Overview

The problem involves calculating the x-component of the electric field due to a line charge represented by a rod on the x-axis with a specified linear charge density. The original poster attempts to find this electric field at the origin using integration.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need for one-dimensional integration to find the x-component of the electric field. There are questions regarding the setup of the integral and the contributions from infinitesimal charge elements.

Discussion Status

The discussion is ongoing, with participants exploring the integration process and clarifying the contributions to the electric field. Some guidance has been offered regarding the approach to summing contributions from the charge elements, but there is no consensus on the integral's setup.

Contextual Notes

There may be assumptions about the limits of integration and the interpretation of the linear charge density that are under discussion. The original poster's calculations and the provided answer differ, indicating potential misunderstandings or misinterpretations of the problem setup.

Arrhenius7991
Messages
8
Reaction score
0

Homework Statement



A rod lies on the x-axis with one end at the origin and another at x=2. The linear charge density is given by λ(x)=C(x^(3) + 3x^(2)). Find the x-component of the electric field Ex at the origin in terms of q.

Homework Equations


Ex = ƩdEx
||dE||= (k|dq|/r^(2)) (z/r)
dq = λ dx


The Attempt at a Solution



I took z = 0 since there is no z dimension. r to be 2 since the rod is 2m long. So Ex = (1/4)kq. But the answer solution says (-2/3)kq.
 
Physics news on Phys.org


Since you only want the x component, this is just a simple one-dimensional integration from one end of the rod to another.
 


I'm not seeing this integral then.
 


You want to add up the contribution to the field from each infinitesimal charge element on the rod.
 

Similar threads

  • · Replies 13 ·
Replies
13
Views
1K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
Replies
1
Views
2K
Replies
9
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
Replies
11
Views
4K
Replies
6
Views
4K
  • · Replies 1 ·
Replies
1
Views
4K
Replies
64
Views
6K