The electromagnetic field, like other fields in physics, is a fundamental concept used to describe the behavior of electromagnetic interactions. According to our current understanding of physics, fields exist within the framework of spacetime.
Spacetime is the four-dimensional continuum that combines space and time into a single entity, as described by Einstein's theory of general relativity. Fields, including the electromagnetic field, are considered to be properties of spacetime. They permeate the entirety of spacetime and interact with particles and other fields.
The concept of fields existing within spacetime is central to our understanding of how particles and forces interact. Fields have values at every point in spacetime and can change over time. Particles, in turn, are excitations or quanta of these fields. For example, photons are particles associated with the electromagnetic field.
While our current understanding suggests that fields are intrinsically tied to spacetime, it's worth noting that our understanding of the nature of spacetime and fields continues to evolve. Theoretical frameworks such as quantum field theory and string theory provide deeper insights into the fundamental nature of fields and spacetime. However, these theories are still subject to ongoing research and refinement, and the precise nature of fields and their relationship to spacetime is an active area of study in theoretical physics.