What Determines the Validity of Modeling a Wire as a Line of Charge?

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The discussion centers on determining the conditions under which a straight wire with a positive charge can be modeled as a line of charge. Key considerations include the relationship between the wire's diameter and its length, with option B suggesting that the diameter must be much smaller than the length for the model to hold. Participants express confusion over the implications of different assumptions, particularly regarding the significance of the wire's diameter. There is a consensus that option A is essential, but uncertainty remains about the relevance of other options. Overall, the focus is on clarifying the criteria that validate the line of charge model for the wire.
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Homework Statement


A straight wire of length has a positive charge distributed along its length. Find the magnitude of the electric field due to the wire at a point located a distance from one end of the wire along the line extending from the wire.
The picture is attached below.



Homework Equations


The wire can be modeled as a line of charge if you assume which of the following?
A) The diameter of the cross section is constant throughout the wire.
B) The diameter of the cross section is much smaller than the length of the wire.
C) The diameter of the cross section has the same order of magnitude as the length of the wire.
D) The cross section has a circular shape.
E) The cross section has a highly symmetrical, though not necessarily circular, shape.




The Attempt at a Solution


The combinations we have tried are ABD, AB, ABE, AD, ACD, ACE, AE. We are pretty sure it's A and were thinking it was D but arent' completely sure. We have come up with numerous reasons for our combinations but keep coming up wrong. If anyone has any idea as to where we are going wrong in our assumptions we would greatly appreciate it.
Thanks so much!
Devon
 

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Forgetting the charge distribution for the moment, which of these assumptions will make the wire look pretty thin and almost one dimensional from a slight distance, if you don't look too closely?
 
We thought about that and chose option B, When we plugged in AB it gave us a response that said that if we chose to do that the diameter then wouldn't matter, which made us think that it was telling us that it should matter.
 
What is the harm if the diameter varies a bit while being very small compared to the length? What was your logic behind choosing A?
 

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