It floats because the current running through the wire charges, or ionizes, some of the surrounding air molecules, building up a big positive charge. Those positively charged molecules are attracted to the negatively charged foil sheet.
The attraction causes the ionized air molecules to move from the wire to the sheet. As they do, they collide with neutral air molecules around them. The collisions are mostly downward, so the result is a flow of air - thrust - that makes the whole thing move upwards.
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Only recently, though, has anyone looked into making it practical for real aircraft. Why? One problem is that the thrust per unit area is low, so the vehicle needs to be light.
Also, since the amount of thrust depends on the voltage, a large aircraft would need a lot of voltage. The science fair project version uses 30,000 volt power supplies (they aren't so dangerous because the currents are small). A real airplane would need hundreds of thousands of times that. The researchers say in a press release that the engine might be close to the size of the airplane itself.