In a static electromagnetic field, both electric and magnetic fields can exist simultaneously, leading to a non-zero Poynting vector, S=ExH, indicating energy flow despite the energy density remaining constant (dU/dt=0). This situation arises when a static magnetic field is generated by a constant electric current, which implies energy is being transferred into matter due to resistance. The conservation of energy is expressed through the equation ∂u/∂t + ∇·S = -J·E, clarifying the relationship between energy density and flux. The concept of "hidden momentum" is mentioned but not elaborated upon, with a recommendation to consult Jackson's book on Electrodynamics for further understanding. Static fields indeed exhibit energy flux, confirming the initial confusion.
