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Re: [Phys-L] treating force as a vector ... consistently



Actually, if there must be reaction, it should probably be applied to the charges producing current in the solenoid, and to their field. This would remove all the previous questions as ill-posed. The resultant of all such forces would be at the center of mass (electron-solenoid), that is practically at the center of the electron orbit.
Moses Fayngold,NJIT

On Saturday, August 27, 2016 5:48 PM, Moses Fayngold <moshfarlan@yahoo.com> wrote:


  I want to add to my previous message another example illustrating limitations of the "action-reaction" concept. Consider a charged point-particle like an electron tracing out a circle in a static homogeneous magnetic field, e.g. within a solenoid with constant current. There is a Lorentz (magnetic) force on the electron. If we identify this force as an "action", an interesting question arises: what is the corresponding "reaction", what is its nature, and to which object and at which location it is applied? My "knee-jerk" answer would be that it has to be magnetic force applied to the center of the circle, pointing at the electron and rotating synchronously with it. But it is obviously wrong. First, the electron's magnetic field at the center is perpendicular to the circle and the corresponding required force would appear only if there is a charged particle there with a specific velocity (anti)parallel to that of the electron. But whatever would be there, it cannot remain at the center while in motion. Second, there would be also electric force on the particle arising from the rotating electric field produced by the electron at the center. Third, there assumed nothing to be at the center! Forth, if the object is extended, the reaction force is assumed to be applied to its center of mass. Considering our object as a rigid sequence (solenoid-the Lab-the Earth) takes us to the center of the Earth. Fifth, in such case both - the Earth's center and the electron must orbit around their common center of mass, which to the highest accuracy is coincident with the Earth's center. Sixth, then the electron's orbit will have nothing to do with initially considered circle inside of the solenoid, and if we insist on the same period, then the electron's velocity may be far above c.  As of now, I do not see satisfactory resolution of this conundrum, except for saying that the "action-reaction" concept does not apply in this situation.  I will appreciate any comments.
Moses Fayngold,NJIT 

On Saturday, August 27, 2016 9:33 AM, Moses Fayngold <moshfarlan@yahoo.com> wrote:


On Saturday, August 20, 2016 8:45 PM, Todd Pedlar <pedlto01@luther.edu> wrote:



As long as I never refer to actions or reactions (I actively oppose this
the first day we talk about forces in my courses) ...
If only the first day, it is OK. But if permanently, then why?
...I specify the following:

1) The two forces which constitute a Newton's Third Law Pair must act on
different bodies
2) They must be of the same kind (friction, gravitation, contact forces, etc)
3) When considering the state of motion of a body, one must consider all
the forces on (and only the forces ON) that body by any other agent
This is an excellent clarification which is frequently lacking in teaching. When a book is resting on a table, there is downward gravitational force (action) on the book from the Earth and the upward gravitational force (reaction) on the Earth from the book. We have a pair of action-reaction forces of the same kind applied to two different bodies. 
 In addition, there is an upward normal force (another action) on the book from the table and the downward normal force (the respective reaction) on the table from the book. Altogether, we have two distinct pairs of action-reactions: one gravitational between book and the Earth, and one normal (contact) between the book and the table. Unfortunately, students often confuse (downward gravitational force on the book + upward normal force on it) with the action-reaction pair. Formally, they are equal and opposite, but they are 1)applied to the same body and 2)are of different kind, which takes them out of "action-reaction" category. One way to clarify the confusion would be, e.g., to push the table upward with some acceleration. Then the normal force on the book, while remaining opposite to the gravity force, would exceed it in magnitude. This shows that they are not action-reaction pair.   But we must also warn the students, at least at some later stage, that the initial simple definition of "action-reaction" works only in the static classical mechanics. Already in Electrodynamics with 2 point charges in relative motion the forces between them are generally neither opposite nor equal in magnitude. In such cases a better description of reality would be momentum of particles and their fields. 
Moses Fayngold,NJIT

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