Late 19th century; earliest use found in Proceedings of the Physical Society of London. Either from electrodynamic + -ally, or from electrodynamical + -ly.
Definition of electrodynamically in US English:
electrodynamically
adverbɪˌlɛtrə(ʊ)dʌɪˈnamɪkli
Physics
By means of electrodynamics.
Origin
Late 19th century; earliest use found in Proceedings of the Physical Society of London. Either from electrodynamic + -ally, or from electrodynamical + -ly.