Imagine that you've been invited to try out a new "hoversuit," and here's how it works:
Someone has set up a large flat sheet, many kilometers across, somewhere on the Earth, and they've charged the sheet up to a uniform charge density σ = +2 x 10^-6 C/m^2. You are issued a special suit that you wear, and it has controls on it which allow you to charge the suit up to any number of Coulombs (C), positive or negative, that you might want. The idea is that you can control the amount of electrical repulsion (or attraction) between the suit and the charged sheet below you.
(a) How much charge (and is it positive or negative) must you give the suit if you want to be able to just hover stationary above the charged sheet? Give your answer in Coulombs (C).
(b) How much charge (and is it positive or negative) must you give the suite if you want to "fall up," that is, accelerate upward at the same rate that objects normally accelerate downward due to Earth's gravity.
(c) How much charge (and is it positive or negative) must you give the suit if you want to fall down toward the sheet, but at the same rate as if you were on the Moon (remembering that the gravitational acceleration on the Moon is 1/6 what it is on Earth)?
The Attempt at a Solution
(a) If this is a parallel plate capacitance problem and the given charge is the bottom plate then the upper plate (the suit), if it is to hover, should have the same charge but negative. This way the two "plates" can remain close without pushing each other away.
-2 x 10^-6 C/m^2
(b) Objects normally accelerate downward toward the Earth at the rate of 9.8 m/sec^2. If the suit is to "fall up", that is, accelerate upward, then it must have a positive charge because then it will be repelled by the positively charged sheet.
(c) On this one, I am totally lost. If the gravitational acceleration on the Moon is 1/6 what it is on Earth, then the rate should be 1.63 m/sec^2.