## 1908 Bucherer Experiment And The Lorentz Force Law

**Authors:** chan Rasjid Kah Chew

The Bucherer experiment of 1908 was not experimental proof of a relativistic mass varying with speed, but proof that electromagnetism and the Lorentz force law fail under relativistic speed conditions. Our conclusions come from a novel re-examination of the experiment based on three different interpretations of New ton’s second law as applied to the experiment and to analyze the
implications for each of:
(1) force∝dp/dt
(2) force=relativistic_mass×acceleration
(3) the classical f = ma
The new interpretation now shows a constant charge-mass ratio for all relativistic speed; both charge and mass would be speed invariant. New relativistic force laws had to be proposed to be
consistent with the experimental findings; the Lorentz force law is now:
F = q((1+v²/c²)√(1-v²/c²) E + √(1-v⁴/c⁴) (v x B) );
the Coulomb’s law is: F = (1+v²/c²)√(1-v²/c²) (1/4πε₀)q₁q₂R/r²;
The Coulomb’s law has an additional scalar factor dependent on the relative velocity between the charges; for small speed, the form is:
F = (1+½v²/c²)(1/4πε₀)q₁q₂R/r²;
This enables the formula for the force between parallel current-carrying conductors:
F_dl = μ₀/(2πR)i₁i₂dl, be derived free of the concept of the magnetic field. A real possibility exists for a formulation of a revolutionary Newtonian electric theory free of magnetism and the Biot-Savart law.Also,the Bucherer experiment could have been an experimental verification of the relativistic Lorentz force law if the predicted speeds of the electrons had been verified through direct time-of-flight measurements.

**Comments:** 12 Pages. English; with Chinese translation

**Download:** **PDF**

### Submission history

[v1] 2018-10-02 02:51:57

[v2] 2018-10-08 13:34:11

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