Griffiths 5.38: Does Special Relativity Apply?

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Homework Help Overview

This discussion revolves around a problem from Griffiths' Electromagnetism textbook, specifically questioning the applicability of special relativity in the context of the problem presented. The original poster expresses uncertainty about the relevance of relativity to the problem, given its placement in Chapter 5.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the necessity of including the problem statement for clarity. There is a suggestion to analyze the problem through the lens of force balance between the magnetic and electric fields. The original poster attempts to derive the pinch force and questions how to calculate the balancing force from positive charges.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and its requirements. Some guidance has been offered regarding the approach to take, particularly in considering force balance, but there is no explicit consensus on the application of special relativity or the solution path.

Contextual Notes

There is a mention of gamma factors, which typically indicate relativity effects, but some participants suggest these may not be central to the problem's solution. The original poster has not provided the full problem statement, which may be limiting the discussion.

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Homework Statement


This question refers to Griffiths E and M book.

Am I supposed to use special relativity to do this problem? It seems out of place in Chapter 5 if I do?

http://www2.andrews.edu/~mattingl/courses/phys431/incomplete_probs_griffiths3ed_w99.PDF

Homework Equations


The Attempt at a Solution

 
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ehrenfest, please include a problem statement in all your posts, otherwise we cannot help you.
 
OK. I included a link.
 
Like I said in the other thread - you probably should copy/paste the problem text, or at least say which page the problem is on.

Usually when gamma factors show up, that means the problem involves a relativity effect, but here that is just a red herring to derive the solution. I'm not 100 percent sure, but I would suggest you think about this problem from the point of view of a force-balance - The pinch from the B-Field versus the electric field trying to keep the wire neutral. The explanation for the ultimately neutral wire does lie in relativity, though.
 
nathan12343 said:
Like I said in the other thread - you probably should copy/paste the problem text, or at least say which page the problem is on.

Usually when gamma factors show up, that means the problem involves a relativity effect, but here that is just a red herring to derive the solution. I'm not 100 percent sure, but I would suggest you think about this problem from the point of view of a force-balance - The pinch from the B-Field versus the electric field trying to keep the wire neutral. The explanation for the ultimately neutral wire does lie in relativity, though.

Yes, I had that idea also, although I could not figure out how to make that explicit. So, I want to calculate the ratio of the positive and negative charge densities so that the pinch force equals the outward force from the positive charges. First, we should calculate the pinch force as a function of distance from the center of the wire. We can use Ampere's Law to do that, right?

[tex]B 2 \pi s = I \pi s^2 = v \rho_{-} \pi s^2[/tex]

[tex]B = v \rho_{-} s/2[/tex]

So on a line of current of length L is [tex]F_{pinch} = v \rho_{-} ^2 L s/2[/tex]

Now, how to we calculate the balancing force i.e. the force due to the positive charges? That I have no idea!
 
anyone?
 
anyone?
 

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