Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- 1 The background to Maxwell's electromagnetic theory
- 2 Mechanical image and reality in Maxwell's electromagnetic theory
- 3 The elaboration of the molecular-vortex model
- 4 The introduction of the displacement current
- 5 The origin of the electromagnetic theory of light
- 6 Beyond molecular vortices
- Conclusion
- Appendix 1 Draft of “On Physical Lines of Force,” a fragment
- Appendix 2 Drafts of “A Dynamical Theory of the Electromagnetic Field”
- Appendix 3 Vortex rotations in a curl-free region
- Notes
- Index
Appendix 3 - Vortex rotations in a curl-free region
Published online by Cambridge University Press: 24 October 2009
- Frontmatter
- Contents
- Preface
- Introduction
- 1 The background to Maxwell's electromagnetic theory
- 2 Mechanical image and reality in Maxwell's electromagnetic theory
- 3 The elaboration of the molecular-vortex model
- 4 The introduction of the displacement current
- 5 The origin of the electromagnetic theory of light
- 6 Beyond molecular vortices
- Conclusion
- Appendix 1 Draft of “On Physical Lines of Force,” a fragment
- Appendix 2 Drafts of “A Dynamical Theory of the Electromagnetic Field”
- Appendix 3 Vortex rotations in a curl-free region
- Notes
- Index
Summary
Figures 4.8 and 4.9a depict schematically the vortex rotations and idle-wheel translations associated with a uniform current density inside of a long, straight wire with uniform circular cross section. Inside the wire, the magnetic field grows linearly with distance from the axis; because of this, neighboring vortices rotate with different angular velocities; this engenders motion of the idle-wheel particles interposed between the vortices, constituting a nonzero current density J; and the inhomogeneity of the magnetic field H is associated with a nonzero value for curl H, which is equal to the nonzero current density J.
Outside of the wire, the H field falls off as 1/r, where r is the distance from the axis [E. R. Peck, Electricity and Magnetism (New York: McGraw-Hill, 1953), 214–17]. One might, at first thought, expect that because of this, neighboring vortices would rotate with different angular velocities, and this would engender motion of the idle-wheel particles, constituting a nonzero current density J. Even though the magnetic field H is inhomogeneous, however, curl H and hence curl ω* are zero outside the wire, and Maxwell's calculation leading to equation (3.7a) shows that in this situation there will be no net flux of the idle-wheel particles, and hence no current ι or J.
- Type
- Chapter
- Information
- Innovation in Maxwell's Electromagnetic TheoryMolecular Vortices, Displacement Current, and Light, pp. 182 - 184Publisher: Cambridge University PressPrint publication year: 1992