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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 Maxwells 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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A uniformly-charged spherical shell of radius $R$, mass $m$, and total electrical charge $q$, having an oscillatory angular velocity $Omega(t)$ around a fixed axis, is a model for a magnetic dipole that radiates an electromagnetic field into its surrounding free space at a fixed oscillation frequency $omega$. An exact solution of the Maxwell-Lorentz equations of classical electrodynamics yields the self-torque of radiation resistance acting on the spherical shell as a function of $R$, $q$, and $omega$. Invoking the Newtonian equation of motion for the shell, we relate its angular velocity $Omega(t)$ to an externally applied torque, and proceed to examine the response of the magnetic dipole to an impulsive torque applied at a given instant of time, say, $t=0$. The impulse response of the dipole is found to be causal down to extremely small values of $R$ (i.e., as $R to 0$) so long as the exact expression of the self-torque is used in the dynamical equation of motion of the spherical shell.
In this tutorial, we discuss the radiation from a Hertzian dipole into uniform isotropic lossy media of infinite extent. If the medium is lossless, the radiated power propagates to infinity, and the apparent dissipation is measured by the radiation resistance of the dipole. If the medium is lossy, the power exponentially decays, and the physical meaning of radiation resistance needs clarification. Here, we present explicit calculations of the power absorbed in the infinite lossy host space and discuss the limit of zero losses. We show that the input impedance of dipole antennas contains a radiation-resistance contribution which does not depend on the imaginary part of the refractive index. This fact means that the power delivered by dipole antennas to surrounding space always contains a contribution from far fields unless the real part of the refractive index is zero. Based on this understanding, we discuss the fundamental limitations of power coupling between two antennas and possibilities of removing the limit imposed by radiation damping.
A decomposition of the angular momentum of the classical electromagnetic field into orbital and spin components that is manifestly gauge invariant and general has been obtained. This is done by decomposing the electric field into its longitudinal and transverse parts by means of the Helmholtz theorem. The orbital and spin components of the angular momentum of any specified electromagnetic field can be found from this prescription.
We show how to derive a consistent quantum theory of radiation reaction of a non-relativistic point-dipole quantum oscillator by including the dynamical fluctuations of the position of the dipole. The proposed non-linear theory displays neither runaway solutions nor acausal behaviour without requiring additional assumptions. Furthermore, we show that quantum (zero-point) fluctuations of the electromagnetic field are necessary to fulfil the second law of thermodynamics.
We construct a novel Lagrangian representation of acoustic field theory that describes the local vector properties of longitudinal (curl-free) acoustic fields. In particular, this approach accounts for the recently-discovered nonzero spin angular momentum density in inhomogeneous sound fields in fluids or gases. The traditional acoustic Lagrangian representation with a ${it scalar}$ potential is unable to describe such vector properties of acoustic fields adequately, which are however observable via local radiation forces and torques on small probe particles. By introducing a displacement ${it vector}$ potential analogous to the electromagnetic vector potential, we derive the appropriate canonical momentum and spin densities as conserved Noether currents. The results are consistent with recent theoretical analyses and experiments. Furthermore, by an analogy with dual-symmetric electromagnetic field theory that combines electric- and magnetic-potential representations, we put forward an acoustic ${it spinor}$ representation combining the scalar and vector representations. This approach also includes naturally coupling to sources. The strong analogies between electromagnetism and acoustics suggest further productive inquiry, particularly regarding the nature of the apparent spacetime symmetries inherent to acoustic fields.
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