Please explain how.
LEDs use 15-20mA of current, whilst electromagnets are almost a short circuit, and will use all the current they can get from power source. You would discharge the lamp's supercap in a split-second, and you would probably not be able to lift a paperclip durind that time.
Sure, you COULD hack the flashlight with more supercaps to make it provide enormous amounts of power(like I once did) and put a resistor in series to limit current, but it would be horribly long to charge, and totally impractical.
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Not enough electricity made to be useful and a magnet sorry.
HOWEVER you can easily make a magnet and use a normal battery.
You'll not get a very strong electromagnet from this power source. If you could pick up a paperclip with it you'd be doing well.
What are you trying to do? Power a magnet with a magnet?For a small version, have a look at this project.