volume | PIER Journals

Abstract

Results are presented for the transverse deflection of an electron beam by a long, straight wire carrying direct current. The experimental deflections are compared with three calculation methods based on the Lorentz force law (field theory) and both the Weber (direct action) and Ritz (emission) force formulae. The Lorentz force calculation is the conventional approach expressed in terms of electric and magnetic field components. By contrast the force formulae of Weber and Ritz do not contain any field vectors relating to E or B. The Weber force is based on direct action whereas the Ritz force expression is based on an emission/ballistic principle and is formulated in terms of a dimensionless constant, λ. The experimental beam deflections are for low speed (non-relativistic) electrons. Good agreement between experiment and theory is demonstrated for each approach. In fact, for the case of an infinitely long wire, all three calculation methods give identical results. Finally, the three approaches are contrasted when applied to the case of high speed electrons.

1. Smith, R. T., F. P. Jjunju, and S. Maher, "Evaluation of electron beam deflections across a solenoid using Weber-Ritz and Maxwell-Lorentz electrodynamics," Progress In Electromagnetics Research, Vol. 151, 83-93, 2015.
doi:10.2528/PIER15021106

2. O’Rahilly, A., Electromagnetic Theory: A Critical Examination of Fundamentals, Vol. 2, Dover Publications, 1965; Also available online: http://archive.org/details/ElectrodynamicsORahilly.

3. Lavenda, B. H., A New Perspective on Relativity: An Odyssey in Non-Euclidean Geometries, World Scientific, 2012.

4. Assis, A. K. T., Weber’s Electrodynamics, Springer, Netherlands, 1994.
doi:10.1007/978-94-017-3670-1

5. Wesley, J. P., "Weber electrodynamics, Part I. General theory, steady current effects," Foundations of Physics Letters, Vol. 3, 443-469, 1990.
doi:10.1007/BF00665929

6. Wesley, J., "Weber electrodynamics, Part II. Unipolar induction, Z-antenna," Foundations of Physics Letters, Vol. 3, 471-490, 1990.
doi:10.1007/BF00665930

7. Wesley, J., "Weber electrodynamics, Part III. Mechanics, gravitation," Foundations of Physics Letters, Vol. 3, 581-605, 1990.
doi:10.1007/BF00666027

8. Hovgaard, W., "Ritz’s electrodynamic theory," Studies in Applied Mathematics, Vol. 11, 218-254, 1932.

9. Hsu, J.-P. and Y. Zhang, Lorentz and Poincare Invariance: 100 Years of Relativity, Vol. 8, World Scientific, 2001.
doi:10.1142/4785

10. Rosser, W. G. V., An Introduction to the Theory of Relativity, 193, Butterworths, London, 1964.

11. Hillas, A. M., "Electromagnetic jet propulsion: Non-Lorentzian forces on currents?," Nature, Vol. 302, 271, 1983.
doi:10.1038/302271a0

12. Kinzer, E. T. and J. Fukai, "Weber’s force and Maxwell’s equations," Foundations of Physics Letters, Vol. 9, 457-461, 1996.
doi:10.1007/BF02190049

13. Smith, R. T., S. Taylor, and S. Maher, "Modelling electromagnetic induction via accelerated electron motion," Canadian Journal of Physics, Vol. 93, 802-806, 2014.
doi:10.1139/cjp-2014-0366

14. Smith, R. T., F. P. M. Jjunju, I. S. Young, S. Taylor, and S. Maher, "A physical model for low-frequency electromagnetic induction in the near field based on direct interaction between transmitter and receiver electrons," Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, Vol. 472, 2016.

15. Maher, S., F. P. Jjunju, and S. Taylor, "Colloquium: 100 years of mass spectrometry: Perspectives and future trends," Reviews of Modern Physics, Vol. 87, 113, 2015.
doi:10.1103/RevModPhys.87.113

16. Gibson, J. R., K. G. Evans, S. U. Syed, S. Maher, and S. Taylor, "A method of computing accurate 3D fields of a quadrupole mass filter and their use for prediction of filter behavior," Journal of the American Society for Mass Spectrometry, Vol. 23, 1593-1601, 2012.
doi:10.1007/s13361-012-0426-7

Dr. Raymond Thomas Smith

Dr. Simon Maher