Electrical fields in theory do transmit at the speed of light. In real systems, wires have capacitance and other effects that slow the propagation. Typical propagation speeds are 0.3 to 0.7 times the speed of light, depending mostly on the wire shape and size, characteristics of wire insulation, and interactions with other conductors.
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Yes, it is. The theory of relativity treats time as the fourth dimension, which has …