Conceptual Questions No.2- Forces between two current elements
Consider two non parallel wires each carrying a current which located at one plane surface.
According to electromagnetic theory, the forces between two straight and solid wires mentioned can be estimated as follow:

F= i . (L x B)

Where the "F" is force vector that applied to each wire and "L" and "B" are current path vector and flux density vector respectively. Also "i" is amount of current and "x" is vector multiply symbol.Therfore the vector of forces are perpendicular to "L" or wires body.
Whereas two wires are not parallel, generally that mentioned forces which applied to wires can not be parallel. As you see we have two piece of material that apply two mutual forces to each other which are not alien and this is inconsistent with Newton's third law seemingly.

#1
Mon, August 31st, 2009 - 10:58
According to electrical engineering experience, two free wires carrying currents can not stable non parallel, and applied electromagnetic torque to each wire rotate them and they will be parallel after short time.Therefor in non parallel configuration of wires we need to assume one supplementary mechanical force in system which we were not considered it.
Of course in free wires moving duty we have involved with problem yet. In that condition because of magnetic field variation, the mass of magnetic field change due to wires moving. Therefore the essential principle of survival momentum is fulfilled and we can forget that inconsistent (action and reaction forces) temporarily.

#2
Mon, August 31st, 2009 - 11:00
The law of conservation momentum is one of essential law in classic and modern physics that shall not contravene. Also as you know the electromagnetic field similar to other forces field is a form of energy and energy is equal to mass, therefore the changing of electromagnetic field cause mass or momentum changing.

#3
Tue, September 23rd, 2014 - 05:23
It's right. But you can't have those segments of wire isolated, so forces on dashed wire will cancel the forces of the solid wires. But it is true that electromagnetic interactions not always obeys newton's laws.

#4
Tue, September 23rd, 2014 - 09:52
The illustrated circuit is a typical case of two interacting current elements which are related together via one common power supply, but my discussion is fundamental and two current elements can be individual generally.

#5
Thu, September 25th, 2014 - 03:17
Yes, as you said, it is a typical case. You can find a similar case: two electron particles in perpendicular trajectories. Again, two interacting current elements can violate 3rd law of Newton, but only because they are a "partial" view and an abstraction. You can't isolate those currents elements, so any complete configuration will always obey  3rd law of motion and conservation laws. So is the case of electrons: they will exert an action and reaction at 90 degrees, violating in that exact instant, the 3rd law of motion but ¿next what? Electrons won't disappear, indeed they, as a closed system, will cancel any net force, so globally 3rd newton law will be obeyed. Maybe I can draw an analogy: Consider a balanced spinning wheel. Take a Little segment of it and call it "mass-current element". This "mass-current element" is exerting an unbalance force on pivot's wheel. But you can't isolate it, and it is not alone, so the complete system is balanced. It doesn't matter if there is a "mass-current element" that is not balanced. I wish it could be isolated and then used!

#6
Thu, September 25th, 2014 - 03:21
(yes I keep writing... :) ) I don't know if I can post a link on this subject, but here we go:http://www.m-hikari.com/astp/astp2012/astp21-24-2012/ansariASTP21-24-2012-2.pdf
This is a formal analysis of the subject. Hope it help.

#7
Thu, September 25th, 2014 - 11:26
Okay, but what is your comment on my description about interacting forces between two non- parallel current elements which flow in two individual conductors?