Can you fill an entire room with a strong magnetic field using current technology?
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Answer it!
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30 second video
15 minute safety video
For starters, I would suggest reading about magnetic levitation. Yes, magnetism might be a lot cooler without Earnshaw's Theorem messing up everybody's great ideas for magnetic gadgets.
But notice those exceptions to it. Examples of using a feedback controller or diamagetism to get around it can be found on Instructables. Then there's the ever-popular cheat of using strings or barriers.
Some especially powerful electromagnets are found in MRI machines (this one is just on standby power!) and research labs.
If you would like to experiment with large permanent magnets, especially of the neodymium type, be sure to look around for a good deal- there are many many rip-offs out there. K&J Magnetics has some reasonably-priced items, as do some of the Ebay sellers who have cheap Chinese knock-offs and readily admit that that's what they sell. Before deciding on any purchase, always calculate the unit price, like dollars per cubic inch of magnet. Like at the grocery store, the bigger ones are usually (but not always) the better deal.
(total price + shipping) / (number in a package) / (volume of each one)
For example
($15.20 + $5) / 2 magnets / .442 cubic inches = $22.85 per cubic inch
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