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I have seen on several books that the expression for the E field generated by an accelerated charge, at enough distance and in the non-relativistic aproximation, is something like that (taken from Jackson):

[Broken]

where "β with the dot above" is the acceleration divided by c,

According to that expression, if the acceleration of the charge oscillates, so does the field, but if the acceleration is constant or varies monotonically, the E field does the same (consider for example an electron accelerating in a rectilinear motion). Does it have any sense?. Can a radiation field be described by a field that is constant (or at least not oscillating)?. There should be something I have misunderstood.

By the way, there is a tendency to interpret always the Poynting vector as an energy flux density in that direction, but this cannot be done in general. Consider for example a static charge near a magnet: the Poynting vector is not zero, but there is no energy flux.

[Broken]

where "β with the dot above" is the acceleration divided by c,

**n**is a vector pointing from the charge to the calculation point, and R is the distance to the charge. Books use this expression (and another one for the B field) to calculate de power irradiated in different directions with the Poynting vector, assuming that we have a radiation field, but... wait a moment!According to that expression, if the acceleration of the charge oscillates, so does the field, but if the acceleration is constant or varies monotonically, the E field does the same (consider for example an electron accelerating in a rectilinear motion). Does it have any sense?. Can a radiation field be described by a field that is constant (or at least not oscillating)?. There should be something I have misunderstood.

By the way, there is a tendency to interpret always the Poynting vector as an energy flux density in that direction, but this cannot be done in general. Consider for example a static charge near a magnet: the Poynting vector is not zero, but there is no energy flux.

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