Relativistic explanation for magnetic force between perpendicular wires

[guillefix]

I have read about how magnetism arises from electric interactions and relativity. But in that respect i don't see how perpendicular wires can exert magnetic forces on each other. The movement of the charges is perpendicular so length contraction does not occurr in the direction of the current for any of the wire electron's reference frames; and, as I have read this is the reason for magnetic forces.

How is this resolved?

Thank you,

 

[tiny-tim]

hi guillefix!

here's an image and commentary from daniel schroeder's 1999 summary lecture from edward purcell's 1960 book (http://physics.weber.edu/schroeder/mrr/mrr.html, link provided by Dalespam ) …

With all this in mind, let's now consider our wire again, but with the test charge moving directly toward it.

In the frame of the test charge the wire is moving downward. The negative charges in the wire, which are moving straight down, have their electric fields distorted as shown previously, but these fields are symmetrical from left to right so they exert no net horizontal force on the test charge. The positive charges in the wire, however, are now moving diagonally, so their fields are distorted as shown above. At the location of the test charge, the field of the positive charge to the right is stronger than that of the positive charge to the left, so the test charge feels a net force pushing it to the left.​

read the whole lecture!

 

[guillefix]

Aah OK, I love diagrams :) So, is the deformation of the E field due to length contraction?

Yep, I'll definitivelly read the whole lecture, it looks really interesting!

 

[truesearch]

This is covered brilliantly in a textbook by Ohanian.

 

[guillefix]

This is covered brilliantly in a textbook by Ohanian.

Is it this one? https://www.amazon.com/dp/0977858278/?tag=pfamazon01-20

 

[truesearch]

Damn... I am not certain... I think it is called physics for engineers...something like that.
I had a copy and lent it to a student (you know the rest of the story!)
Ohanian textbooks are the best I have come across. I imagine the analysis is in the one you quote but I am not certain... I will get on Amazon and have a look
I have not looked at tiny tims reference yet but it looks good... I will look at it.

 

[truesearch]

Tiny Tims reference is great... Ohanian includes more detail and more depth but the principle is the same.

 

[guillefix]

Ok, id still like to know the book by Ohanian if you find it. BTW, would The Feynman lectures have a good explanation because I a copy of them. Anyway I'll find out coz I want to finish them soon :)