Actually the S-Pen is powered by the electromagnetic grid under the display of the SGTS4. There is a very small electromagnetic device in the pen, which picks up power from the grid underneath the glass.
had to correct this years later:
and inductive stylus in not "powered" at all. passivly interact with the magnetic field of the device youre using it on
a bluetooth-stylus with a battery does not requere charging for regular functioning but for the bluetooth functionality like making photos. your regular stylus-activitys are not effected in any way. dont want to chard: dont use the bluetooth function so you dont need it. the stylus itself is passive