Energy possessed by Electric Field

[IEVaibhov]

Consider a parallel plate capacitor.
It is said that electromagnetic waves store electrical energy.
Since electromagnetic waves don't require a medium to propogate, we can say that electrical energy can be stored in a space where there are no medium particles (say vaccuum).
Where exactly is electrical energy stored? It is not so intuitive.

 

[granpa]

in the field itself.

in fact the energy is proportional to the square of the field.

 

[JeffKoch]

You can think of it in various ways, but you did work to separate the charges and build up the field between the plates, so I think of that energy being stored in the separated charges, i.e. potential energy.