Question

While the movie back to the Future II came out everyone wanted a hover-board. You decide to use your information of electrostatics to finally make this dream come true. You plan to build a room with an electrically charged floor where someone standing on an electrically charged hover-board can levitate four inches above the ground. Assume you are able to achieve a charge density on the floor of 10-3 C/m2.

a) What net charge do you require on the hover-board in order to be able to levitate above the floor?

b) What will voltage difference be between floor and hover-board? Suppose hover-board is levitating four inches above the floor.

c) Look up dielectric breakdown of air. How does ΔV/Δx between the hover-board and floor compare to the dielectric breakdown of air? Why is this important comparison to make? Note- Dielectric breakdown is a new concept that we have not talked about. I literally want you to Google ‘dielectric breakdown of air’ to find its value and learn what it means.

This question requires you to estimate some values and make some assumptions. You must explicitly state in your solution any assumptions you are making. You would be graded on both your use of physics and organization and coherence of your work. You would probably need to write down a few sentences here and there to make sure grader can understand your thought process.