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Electrostatic approximation

The validity of the electrostatic approximation rests on the assumption that the electric field is irrotational:

From Faraday's law, this assumption implies the absence or near-absence of time-varying magnetic fields:

In other words, electrostatics does not require the absence of magnetic fields or electric currents. Rather, if magnetic fields or electric currents do exist, they must not change with time, or in the worst-case, they must change with time only very slowly. In some problems, both electrostatics and magnetostatics may be required for accurate predictions, but the coupling between the two can still be ignored. Electrostatics and magnetostatics can both be seen as non-relativistic Galilean limits for electromagnetism. In addition, conventional electrostatics ignore quantum effects which have to be added for a complete description.