scholarly journals Newton &-vs Lorentz

2018 ◽  
Vol 14 (3) ◽  
pp. 5869-5872
Author(s):  
Armando Tomas Canero
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Classical Mechanics ◽  
Classical Field Theory ◽  
Classical Field ◽  
The Body ◽  
Circular Path ◽  
Third Law ◽  
A Minor ◽  
The Magnetic Field

Is there a point of divergence between Classical Mechanics and Electromagnetism? This discrepancy is raised by many authors and arises between Newton's third law and the equation of Lorentz forces. Due to the transcendence of these expressions, their wide application in different situations is not a minor issue and should be given a consistent interpretation with both theories. The discrepancy mentioned is based in that: according to the calculations of classical field theory, a particle with an electric charge moving immersed in a magnetic field suffers an action that diverts its trajectory, making it describe a circular path, which can not be compensated through a contrary force in the body that generated the magnetic field. The force on this second body is predicted, by this theory, at ninety degrees from the first, thus contradicting the principle of action and reaction. This study shows why the Lorentz law does not contradict Newton's third law and gives a consistent explanation of how the equations of classical field theory should be applied so that the result is correct.

Elements of Classical Field Theory

2021 ◽  
pp. 24-34
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Field Theory ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Classical Field Theory ◽  
Classical Field ◽  
Lagrange Equations ◽  
Lie Group Of Transformations ◽  
Infinitesimal Transformations ◽  
Conserved Currents

The purpose of this chapter is to recall the principles of Lagrangian and Hamiltonian classical mechanics. Many results are presented without detailed proofs. We obtain the Euler–Lagrange equations of motion, and show the equivalence with Hamilton’s equations. We derive Noether’s theorem and show the connection between symmetries and conservation laws. These principles are extended to a system with an infinite number of degrees of freedom, i.e. a classical field theory. The invariance under a Lie group of transformations implies the existence of conserved currents. The corresponding charges generate, through the Poisson brackets, the infinitesimal transformations of the fields as well as the Lie algebra of the group.

scholarly journals Asymptotic Conservation Laws in Classical Field Theory

1996 ◽  
Vol 77 (20) ◽  
pp. 4109-4113 ◽  
Author(s):  
Ian M. Anderson ◽  
Charles G. Torre
Keyword(s):  
Field Theory ◽  
Conservation Laws ◽  
Classical Field Theory ◽  
Classical Field

Emerson's Atom and the Matter of Suffering

2009 ◽  
Vol 64 (1) ◽  
pp. 16-47
Author(s):  
Mark Noble
Keyword(s):  
Field Theory ◽  
Natural History ◽  
Classical Field Theory ◽  
Classical Field ◽  
The Other ◽  
History Of ◽  
The One ◽  
The Individual ◽  
Solid Bodies ◽  
Lines Of Force

This essay argues that Ralph Waldo Emerson's interest in the cutting-edge science of his generation helps to shape his understanding of persons as fluid expressions of power rather than solid bodies. In his 1872 "Natural History of Intellect," Emerson correlates the constitution of the individual mind with the tenets of Michael Faraday's classical field theory. For Faraday, experimenting with electromagnetism reveals that the atom is a node or point on a network, and that all matter is really the arrangement of energetic lines of force. This atomic model offers Emerson a technology for envisioning a materialized subjectivity that both unravels personal identity and grants access to impersonal power. On the one hand, adopting Faraday's field theory resonates with many of the affirmative philosophical and ethical claims central to Emerson's early essays. On the other hand, however, distributing the properties of Faraday's atoms onto the properties of the person also entails moments in which materialized subjects encounter their own partiality, limitation, and suffering. I suggest that Emerson represents these aspects of experience in terms that are deliberately discrepant from his conception of universal power. He presumes that if every experience boils down to the same lines of force, then the particular can be trivialized with respect to the general. As a consequence, Emerson must insulate his philosophical assertions from contamination by our most poignant experiences of limitation. The essay concludes by distinguishing Emersonian "Necessity" from Friedrich Nietzsche's similar conception of amor fati, which routes the affirmation of fate directly through suffering.

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