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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 asthe radiated electromagnetic field in the surrounding free space. The assumedgeometry enables us to obtain the exact solution of Maxwell's equations as afunction of the dipole moment, the sphere radius, and the oscillationfrequency. The self field, which is responsible for the radiation resistance,does not introduce acausal or otherwise anomalous behavior into the dynamics ofthe bound electrical charges that comprise the dipole. Departure fromcausality, a well-known feature of the dynamical response of a charged particleto an externally applied force, is shown to arise when the charge is examinedin isolation, namely in the absence of the restraining force of an equal butopposite charge that is inevitably present in a dipole radiator. Even in thiscase, the acausal behavior of the (free) charged particle appears to be rootedin the approximations used to arrive at an estimate of the self-force. When theexact expression of the self-force is used, our numerical analysis indicatesthat the impulse-response of the particle should remain causal.

Electromagnetic radiation and the self field of a spherical dipole oscillator