Griffiths Problem 5.38

[ehrenfest]

1. 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]


2. Homework Equations



3. The Attempt at a Solution

 

[Hootenanny]

ehrenfest, please include a problem statement in all your posts, otherwise we cannot help you.

 

[ehrenfest]

OK. I included a link.

 

[nathan12343]

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.

 

[ehrenfest]

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?

$$B 2 \pi s = I \pi s^2 = v \rho_{-} \pi s^2$$

$$B = v \rho_{-} s/2$$

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

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

 

[ehrenfest]

anyone?

 

[ehrenfest]

anyone?