The energy of electric and magnetic fields is indeed dependent on their sources, as they are generated by the flow of electrons. When an electromagnet is powered and the current is increased, energy is stored in the magnetic field. Upon switching off the current, the collapsing field induces a new electron flow, which can result in a spark across the switch. This phenomenon illustrates the relationship between the source of the field and the energy dynamics involved. Understanding this interaction is crucial in the study of electromagnetism.