Circular motion of a charged particle in an electric dipole field

Jones, Randall S.

doi:10.1119/1.18026

Cited by 9 publications

(13 citation statements)

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“…The electron oscillates along a semicircle located in a meridional plane in the upper hemisphere. (This is analogous to the corresponding result by Jones [7], later reproduced by McDonald [8], for a positive charge: the only difference is that for the positive charge, the semicircular orbit is in the lower hemisphere.) Let us study this special case in more detail before proceeding to the general case.…”

Section: Classical Non-circular Orbitssupporting

confidence: 87%

“…This polynomial has a negative minimum equal to −K − 2/3 3/2 at x = − 1/3 1/2 and a maximum equal to −K + 2/3 3/2 at x = 1/3 1/2 . Obviously, for the range of the bound motion to exist, the maximum should be positive, leading to the following requirement (Fox [6]): K < 2/3 3/2 = K max (7) or equivalently (see Equation (4)…”

Section: Classical Non-circular Orbitsmentioning

confidence: 99%

“…In 1996, McDonald [8] focused at two types of circular (or semicircular) orbits. One type was the same as that presented by Jones [7]. Another type was a circular orbit along a certain parallel of latitude.…”

Section: Introductionmentioning

confidence: 97%

“…In 1995, Jones [7] derived analytical results for a semicircular orbit along a meridian on a sphere, to which the motion is confined (confined according to Fox result [6]). He considered the moving particle to be positively charged and pointed out that its motion is identical to the motion of a pendulum: the potential of a simple pendulum is identical to the potential of the dipole at a constant radius.…”

Section: Introductionmentioning

confidence: 99%

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Oscillatory-Precessional Motion of a Rydberg Electron Around a Polar Molecule

Oks

2020

Symmetry

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We provide a detailed classical description of the oscillatory-precessional motion of an electron in the field of an electric dipole. Specifically, we demonstrate that in the general case of the oscillatory-precessional motion of the electron (the oscillations being in the meridional direction (θ-direction) and the precession being along parallels of latitude (φ-direction)), both the θ-oscillations and the φ-precessions can actually occur on the same time scale—contrary to the statement from the work by another author. We obtain the dependence of φ on θ, the time evolution of the dynamical variable θ, the period Tθ of the θ-oscillations, and the change of the angular variable φ during one half-period of the θ-motion—all in the forms of one-fold integrals in the general case and illustrated it pictorially. We also produce the corresponding explicit analytical expressions for relatively small values of the projection pφ of the angular momentum on the axis of the electric dipole. We also derive a general condition for this conditionally-periodic motion to become periodic (the trajectory of the electron would become a closed curve) and then provide examples of the values of pφ for this to happen. Besides, for the particular case of pφ = 0 we produce an explicit analytical result for the dependence of the time t on θ. For the opposite particular case, where pφ is equal to its maximum possible value (consistent with the bound motion), we derive an explicit analytical result for the period of the revolution of the electron along the parallel of latitude.

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Section: Classical Non-circular Orbitssupporting

confidence: 87%

Section: Classical Non-circular Orbitsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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Oscillatory-Precessional Motion of a Rydberg Electron Around a Polar Molecule

Oks

2020

Symmetry

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“…The conditions for motion in a plane containing d are also obtained and several previous results are recovered. [1][2][3][4] …”

Section: Introductionmentioning

confidence: 99%

A new constant of motion for an electric charge acted on by a point electric dipole

Gutiérrez-López

Castellanos-Moreno

Rosas-Burgos

2008

American Journal of Physics

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Quantitative analysis of the damping of magnet oscillations by eddy currents in aluminum foil Am. J. Phys. 80, 804 (2012) Rolling magnets down a conductive hill: Revisiting a classic demonstration of the effects of eddy currents Am. J. Phys. 80, 800 (2012) A semiquantitative treatment of surface charges in DC circuits Am. J. Phys. 80, 782 (2012) Relation between Poisson and Schrödinger equations Am. J. Phys. 80, 715 (2012) Magnetic dipole moment of a moving electric dipole Am.

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