Griffiths Problem 5.38

1. The problem statement, all variables and given/known data
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. Relevant equations



3. The attempt at a solution

 

OK. I included a link.

 

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?