Receding Electric field/Magnetic Field?

In a circuit, would the electric field produced by emf instantly go to zero upon disconnecting the circuit from the emf source? I would assume there is some sort of time delay. If so, what is it?

Similar question for a magnetic field: if a conducting solenoid producing a magnetic field is removed from its emf source, how fast would its magnetic field go to zero? I read something about magnetic field decay somewhere, and this article cites 30-thousandths of a second:

http://newscenter.lbl.gov/news-relea...atter-up-down/

Thanks.