Max von Laue

Name: On the Theory of the Experiment of Trouton and Noble
Author: Max von Laue

On the Theory of the Experiment of Trouton and Noble

Summary

“On the Theory of the Experiment of Trouton and Noble”, is a work by Max von Laue. It explores elements such as torque, condenser and plates.

Quotes from On the Theory of the Experiment of Trouton and Noble (Max von Laue)

Max von Laue, On the Theory of the Experiment of Trouton and Noble

“ The subject of the experiment is the question, whether a charged plate condenser experiences a torque due to its motion with Earth. Relativity and absolute theory accordingly are affirming this; of course, relativity theory does this only in the case of a non-co-moving reference system ; in the "rest system" there is no torque. With the absolute theory, we can now expect a rotation in consequence of the torque, since its dynamics is that of Newton; according to this theory, the condenser tries to locate itself, so that the direction of velocity is tangential to the plates. ”

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Source: Wikisource

Max von Laue, On the Theory of the Experiment of Trouton and Noble

“ First we calculate the forces exerted upon the resting condenser. Attraction is the by far strongest force-action exerted by the plates upon each other; it has (as far as the field in the interior can be considered as homogeneous) the strength per unit area, when is the field strength. If we neglect the marginal effects, then these forces produce the resultants of strength
whose points of contact are the midpoints of the plates. Far less strong, but still useful for our purposes, are the traction-forces acting at the rim of the plates. ”

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Source: Wikisource

Max von Laue, On the Theory of the Experiment of Trouton and Noble

“ If we would extend our investigation to this case, we would be faced with great mathematical difficulties, because one cannot use the solution of Helmholtz (section III) for the potential function at the rim any more. Our result can only qualitatively be transferred, so that forces are acting at the rim and the boundary of the dielectric (besides the attraction of the plates) which are tangentially stressing the plates in the state of rest, so that the totality of these forces produces the torque in the case of motion. ”

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Source: Wikisource

Max von Laue, On the Theory of the Experiment of Trouton and Noble

“ Yet it was explained by the author [3] on many occasions, that according to relativity theory, this torque causes no change of motion because the material parts of the condenser (like all elastically stressed bodies) require a torque for uniform translatory motion; at this place, only the procedure shall be considered, by which that torque is calculated in both theories. ”

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Source: Wikisource

Max von Laue, On the Theory of the Experiment of Trouton and Noble

“ Now, as to the forces acting upon the condenser of Fig. 4, they are of course of different amount than the one calculated with respect to Fig. 2. For example, the forces in and as well as and are still mutually equal, but the force in is stronger than the one in . The positive torque exerted by these four forces around the -axis is compensated by the fact, that the forces perpendicular to the plates are not lying in one line as in Fig. 2 any more. Although their contact points (as shown by a simple consideration) are lying nearer at and than at and , they must produce a negative torque. ”

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Source: Wikisource

Max von Laue, On the Theory of the Experiment of Trouton and Noble

“ From the difference of these pressures, the force (parallel to the plates due to reasons of symmetry) is given:
where the integration over the whole force line is to be extended from the plate upon potential , to the one of potential . is the outermost normal of the limiting surface. ”

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Source: Wikisource

Max von Laue, On the Theory of the Experiment of Trouton and Noble

“ If we lay the -axis in the symmetry line of Fig. 1, and if we choose the origin so that the plates form that part of lines reaching from to , and if we also denote the potential function by and the potential difference of the plates by (the line corresponds to the plate of potential ) , then the cited solution of Helmholtz is contained in the equation:
or in the equivalent relations:
The curves =const. are the force lines. The force acting upon the line element of a contour line imagined as conductive, amounts to
and has the direction , when is the perpendicular of directing to the outside. ”

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Source: Wikisource

Max von Laue, On the Theory of the Experiment of Trouton and Noble

“ The forces (mentioned at the end of section II) acting upon the center of the sides of length , are parallel to and remain parallel to at the transformation, as well as the connecting line of their contact points. ”

Max von Laue

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Quotes from On the Theory of the Experiment of Trouton and Noble (Max von Laue)

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