How to intuitively think of energy stored in a magnetic/electric field?
Kindly answer in a bit simple terms without referring to mathematics.
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Energy is a scalar quantity, a single number, that doesn't change in physical systems where all interactions are inside the system.
For a number of particles that only interact with one another at the same location, kinetic energy is this single number that's conserved. When they interact at a distance via the electromagnetic field, the total kinetic energy of the particles is no longer conserved. However, we can still add a quantity associated with the electromagnetic field; electromagnetic energy, to the total kinetic energy of the particles, that still gives us a conserved number called the total energy.
It turns out that the electromagnetic energy is a mathematical expression involving the electric and magnetic fields evaluated over the whole of space, whereas the kinetic energy of a particle is evaluated at one location. Hence there is this picture some people have of electromagnetic energy being "stored" in the electromagnetic field. This is just a confusing, outdated interpretation, influenced by the past when this electromagnetic energy was once seen as stored in an electromagnetic substance called the ether.