Reflection
In the 1800s there was heated debate over whether “the electric field” was a genuine physical entity or just a convenient mathematical trick for calculating forces. The discussion seems idle, but it has enormous implications: if the field is merely a calculation, charges act at a distance; if it is a physical entity, the force is transmitted locally, at a finite speed.
Maxwell, with his equations, and then Einstein, with relativity, gave the answer: the field is a thing. It has energy, it has momentum, it propagates at speed . When in this chapter we speak of “field energy density” we are not using a metaphor: we are saying that space, wherever there is a field, contains energy just as a glass contains water.
This is perhaps the most important conceptual revolution of nineteenth-century science. The vacuum stops being a passive stage and becomes itself a physical reservoir: full of field, and hence full of energy, momentum, and its own dynamics. From here on, physics no longer speaks only of particles, but of fields that live, propagate and carry things — even in the absence of any matter.
Links
Topics: Electric field and potential Concepts: Field energy density · Electric field
Related exercises: Fermi estimate — energy of a cloud · Energy density in a thunderstorm · Shielding and charge in a hollow conductor