Griffiths 5.38: Does Special Relativity Apply?

  • Thread starter ehrenfest
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In summary, the problem is trying to calculate the force due to the positive charges, but the solution can be found in relativity.
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ehrenfest
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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 [Broken]

Homework Equations


The Attempt at a Solution

 
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  • #2
ehrenfest, please include a problem statement in all your posts, otherwise we cannot help you.
 
  • #3
OK. I included a link.
 
  • #4
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.
 
  • #5
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!
 
  • #6
anyone?
 
  • #7
anyone?
 

1. What is Griffiths 5.38 in the context of special relativity?

Griffiths 5.38 refers to a specific problem or exercise in the textbook "Introduction to Electrodynamics" by David J. Griffiths. It pertains to the application of special relativity to the transformation of electric and magnetic fields between different reference frames.

2. Why is it important to study the application of special relativity to electromagnetic fields?

This is crucial because special relativity provides a framework for understanding the behavior of electric and magnetic fields in different inertial reference frames. It helps us understand the nature of electromagnetic phenomena and how they are affected by relative motion.

3. How does special relativity affect the transformation of electric and magnetic fields?

Special relativity introduces the concept of Lorentz transformations, which describe how measurements of electric and magnetic fields change between reference frames moving at different velocities. This includes the effects of time dilation and length contraction on the fields.

4. Can you provide an example of applying special relativity to an electromagnetic field?

One example is the observation of a moving charged particle from different reference frames. The electric and magnetic fields measured by an observer in the particle's rest frame will be transformed when observed by an observer in a different inertial frame due to their relative motion.

5. Is the application of special relativity to electromagnetic fields limited to theoretical concepts?

No, the principles of special relativity have been experimentally confirmed and are crucial for the development and application of technologies such as particle accelerators, GPS systems, and nuclear reactors.

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