I have a solenoid which has a current passing through it which increases linearly with time. I have proved that the energy stored in the magnetic field is equal to the energy being pumped in according to the surface integral of the poynting vector. This implies the energy stored in the electric field is zero (according to poynting's theorem which states the energy change for an EM system is the energy pumped into the E and B fields minus the energy flowing out of the surface in the poynting vector). Why is the energy stored in the electric field zero? My attempt was that in a static situation (constant current I), the energy is entirely in the magnetic field since there is no electric field, so if we take this linear increase in a quasi-static manner, then the energy stored in each quasi-static situation should be equivalent to the same static situation, so it wouldn't make sense if energy was stored in the E-field in one situation but not in the other.