Electric field and charge density

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Homework Help Overview

The problem involves a uniform line charge with a specified charge density located along the x-axis, and it requires finding the electric field at a specific point based on known values at another point. The context is rooted in electrostatics and electric fields.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need to establish a relationship between the electric fields at different distances from the line charge. There are attempts to derive an integral for the electric field due to the line charge and questions about the variables involved, such as the total charge and the distance.

Discussion Status

The discussion is ongoing, with participants exploring different approaches to derive the electric field. Some have suggested using integrals to relate the electric field at different points, while others are questioning the assumptions and variables involved in their calculations.

Contextual Notes

There is uncertainty regarding the value of L and how it influences the electric field calculations. Participants are also considering the implications of the known electric field at 2L to infer information about the field at 3L.

peaceandlove
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Homework Statement


A uniform line charge of density λ lies on the x-axis between x=0 and x=L. Its total charge is 11 nC. The electric field at x=2L is (500 N/C)ˆı. Find the electric field at x=3L. Answer in units of N/C.

Homework Equations





The Attempt at a Solution


I have no clue where to even begin...I know that eventually I need to obtain a relationship between E(2L) and E(3L) but besides that I'm totally lost.
 
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peaceandlove said:

Homework Statement


A uniform line charge of density λ lies on the x-axis between x=0 and x=L. Its total charge is 11 nC. The electric field at x=2L is (500 N/C)ˆı. Find the electric field at x=3L. Answer in units of N/C.

Homework Equations



The Attempt at a Solution


I have no clue where to even begin...I know that eventually I need to obtain a relationship between E(2L) and E(3L) but besides that I'm totally lost.

Develop an integral for a charged line segment along the x-axis. Won't that then tell you what the relationship between distance along x and field strength?
 
I can't seem to get the integral right... I got (1/4(pi)e_0)*(qQ/(d(d+L)). Perhaps I calculated it wrong because I'm not sure what q is.
 
peaceandlove said:
I can't seem to get the integral right... I got (1/4(pi)e_0)*(qQ/(d(d+L)). Perhaps I calculated it wrong because I'm not sure what q is.

What you don't know is what L is.

By giving you the field intensity at 2L, then they are telling you what it is. But rather than calculate it out I'd just go to the ratio and figure the L based on the ratio of the dependency on L.

For instance you should get a result based on the charges being arranged 1L to 2L, and when measured at 3L, the field will be evaluated with the charges 2L to 3L away.
 
Do I do that using the integral I developed? And if so does that mean the one I came up with is correct?
 
peaceandlove said:
Do I do that using the integral I developed? And if so does that mean the one I came up with is correct?

Sorry, I didn't work out your integral. I simply note that you should have an equation of the form

E = kλ∫ 1/r2 = - K/r

where K is the grouped constants (which will cancel out) and r is evaluated from 1 to 2, or 2 to 3.
Then take the ratio of the equations right?

E3/500 = (K*(1/2 - 1/3))/(K*(1-1/2)
 

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