TY - JOUR

T1 - Electromagnetic radiation and the self-field of a spherical dipole oscillator

AU - Mansuripur, Masud

AU - Jakobsen, Per K.

N1 - Funding Information:
The authors express their gratitude to Vladimir Hnizdo for commenting on an early draft of this paper and for generously sharing with us his extensive knowledge of the electrodynamics of charged particles. The authors also thank the anonymous referees whose constructive criticism has substantially improved the pedagogical aspects of this paper. This work was supported in part by AFOSR Grant No. FA9550-19-1-0032.
Publisher Copyright:
© 2020 American Association of Physics Teachers.

PY - 2020/9/1

Y1 - 2020/9/1

N2 - For an oscillating electric dipole in the shape of a small, solid, uniformly polarized, spherical particle, we compute the self-field as well as the radiated electromagnetic field in the surrounding free space. The assumed geometry enables us to obtain the exact solution of Maxwell's equations as a function of the dipole moment, the sphere radius, and the oscillation frequency. The self-field, which is responsible for the radiation resistance, does not introduce acausal or otherwise anomalous behavior into the dynamics of the bound electrical charges that comprise the dipole. Departure from causality, a well-known feature of the dynamical response of a charged particle to an externally applied force, is shown to arise when the charge is examined in isolation, namely, in the absence of the restraining force of an equal but opposite charge that is inevitably present in a dipole radiator. Even in this case, the acausal behavior of the (free) charged particle appears to be rooted in the approximations used to arrive at an estimate of the self-force. When the exact expression of the self-force is used, our numerical analysis indicates that the impulse response of the particle should remain causal.

AB - For an oscillating electric dipole in the shape of a small, solid, uniformly polarized, spherical particle, we compute the self-field as well as the radiated electromagnetic field in the surrounding free space. The assumed geometry enables us to obtain the exact solution of Maxwell's equations as a function of the dipole moment, the sphere radius, and the oscillation frequency. The self-field, which is responsible for the radiation resistance, does not introduce acausal or otherwise anomalous behavior into the dynamics of the bound electrical charges that comprise the dipole. Departure from causality, a well-known feature of the dynamical response of a charged particle to an externally applied force, is shown to arise when the charge is examined in isolation, namely, in the absence of the restraining force of an equal but opposite charge that is inevitably present in a dipole radiator. Even in this case, the acausal behavior of the (free) charged particle appears to be rooted in the approximations used to arrive at an estimate of the self-force. When the exact expression of the self-force is used, our numerical analysis indicates that the impulse response of the particle should remain causal.

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U2 - 10.1119/10.0001348

DO - 10.1119/10.0001348

M3 - Article

AN - SCOPUS:85091975194

VL - 88

SP - 693

EP - 703

JO - American Journal of Physics

JF - American Journal of Physics

SN - 0002-9505

IS - 9

ER -