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Electrical riddle no.6 – Forces between two current elements and Newton's third law
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.

What is your opinion?
Author : Hamid - From: Iran
Mon, October 1, 2007 - 16:33
Basic definition

The classical definition of angular momentum as  L=r× p depends on six numbers: rx, ry, rz, px, py, and pz. Translating this into quantum-mechanical terms, the Hiesienberg uncertainity principle tells us that it is not possible for all six of these numbers to be measured simultaneously with arbitrary precision. Therefore, there are limits to what can be known or measured about a particle's angular momentum. It turns out that the best that one can do is to simultaneously measure both the angular momentum vector's magnitude and its component along one axis.
Mathematically, angular momentum in quantum mechanics is defined like momentum- not as a quantity but as an operator on the wave function:
L=r× p where r and p are the position and momentum operators respectively. In particular, for a single particle with no electric charge and no spin, the angular momentum operator can be written in the position basis as
L=-iλ(r×Δ) where Δ  is the gradient operator, read as "del," "grad," or "nabla". This orbital angular momentum operator is the most commonly encountered form of the angular momentum operator, though not the only one. It satisfies the following commutation relations
,[Li,LJ>=iλ εijk Lkwhere εijk is the (antisymmetric) Levi-Civita symbol.
Author : Greg
Mon, October 1, 2007 - 16:38
I think we shall try to transfer our knowledge content to others by easiest form. Indeed the information package isn't knowledge and it shall be reproduced by creative thinking by others.
Please kindly explain conclusion of your mathematical discussion with easier language.
Also I think we can find problem answer in classical physics or electrical engineering field too.

Author : Hamid - From: Iran
Mon, October 1, 2007 - 16:39
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.

What is your opinion?
Author : Hamid - From: Iran
Mon, October 1, 2007 - 16:43
I dont understant. Why dont you answer clearly ? if you know the answer. 
Author : alvaros
Mon, October 1, 2007 - 16:44
Our main discussion (in electrical engineering field) is regarded static condition of system. But about your comment, I can add as follows:

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.
Author : Hamid - From: Iran
Wed, October 9th, 2013 - 07:07
kindly elaborate the initial problem.

i understood that two wires shown in the figure would eventually be parallel to each other, but i didn't understand how the newton's third law is violated here.

please explain.. 
Author : piyush - From: India
Wed, October 9th, 2013 - 08:32
According to newton's third law, for every action, there is an equal and opposite reaction.
The statement means that in every interaction, there is a pair of forces acting on the two interacting objects. The size of the forces on the first object equals the size of the force on the second object. The direction of the force on the first object is opposite/parallel to the direction of the force on the second object. Forces always come in pairs - equal and opposite/parallel action-reaction force pairs.
But in two non parallel carrying current the reaction forces between two wires is not opposite/parallel.
Author : Hamid - From: Iran
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