Question

In the most basic way possible, and with as little math as possible, what does it mean for energy to be stored in a field? Does this mean that as a charge, say, repulses or attracts another charge, energy is transferred through the fields, and hence physical contact does not have to be made? I’m not sure if this is correct, but either way, can you elaborate (specifically relating to EM).

Answer 1

A field is a difficult concept to be grasped, and then to assign energy to that field is even more difficult. In context of electromagnetism be it an electric field or magnetic filed or a wave comprising both, the fields have some definite spatial and temporal dependence. You must know from the knowledge of electromagnetism that the the energy stored in the filed is given by and . One can grasp the concept of energy stored in following way:

In order to create the fields in the way the behave spatially and temporally some work had to be done. The way the fields vary in space and time carries an imprint of the work done accordingly, and we say that the energy of the work done is transferred to the fields, and hence they carry momentum and energy.