Acceleration without radiation

Abstract

We study the radiation generated by electric currents in (1) infinite cylinders with longitudinal flow, (2) infinite cylinders with solenoidal flow, and (3) infinite planes. In each case we work out four specific examples, for which the retarded fields can be calculated exactly, and we derive a "Larmor-like" formula for the power radiated, in the limit of infinitesimal cross-section. We then consider sinusoidal currents with finite cross-section, and discover that for certain special frequencies the external fields are zero and there is no radiation. We relate our results to the work of Goedecke and others, and conclude with some remarks on the radiation reaction in these configurations.

The fields outside a long solenoid with a time-dependent current

“…The major qualitative result of the present analysis is the same as that of Abbott and Griffiths [2]: the fields outside a solenoid include electromagnetic radiation for a short time after the current starts to flow. Is this radiation in fact detectable?…”

“…If we applied the approximations of Abbott and Griffiths [2] to the direct calculation of E θ then we would obtain only the first term of eq. (24) but with z − being called z 0 .…”

“…The power radiated per unit length by the solenoid at time t 0 measured at the solenoid can be found from the Poynting vector, S = (c/4π)E × B, by integrating it over a large cylinder of radius r at time t = t 0 + r/c [2]:…”

“…This case was treated by Abbott and Griffiths [2] who used the retarded potentials to deduce the following expressions for the fields E and B at the point (r, 0, 0) in cylindrical coordinates (r, θ, z) outside a solenoid with linearly rising current, I = αt per unit length:…”

Homotopy and Path Integrals in the Time-dependent Aharonov-Bohm Effect

“…This shows that must be zero outside the solenoid andḟ = 0. We remark that this kind of field has been shown to have peculiar properties with respect to radiation as well [23].…”