Consider a wire, if I suddenly pass current on it. There would be an instant localized B field around the wire. Since there is sudden change of B field, there will also be a finite E field. According to Maxwell equation E=B/c. As the B field spread out the E field will follow, even when the current is stable and B field stop changing the E field will still be there with the B field. But this has got to be wrong right? Otherwise whenever we turn on a solenoid there will be an observable E field around it!!??