Retarded potentials and radiation of a rotating charged rod

Abstract

In this paper we determine the electromagnetic properties of a rotating charged rod, which rotates around the x-axis with an angular frequency that it’s not constant. As the charge is changing its position over time, the electromagnetic information reaches us with a certain time lag. Therefore, it is necessary to obtain the time-dependent(retarded) potentials at any point in space, for which we need multipolar expansion to determine the field at any point in space and do a Taylor expansion of the distance at which we want to measure the electromagnetic fields, in the static and induction zone. Then, we determine the Poynting vector in the corresponding radiation zone. Finally, we determine the radiated power, emphasizing the symmetries of the problem and showing how we can approach its solution considering these symmetries. .