It is a little ambiguous what exactly is being asked. Constant velocity implies no net force, so your question makes me think about terminal velocity which is established through air resistance, or some sort of friction between the wire and something else. Alternatively, perhaps a counter...
Is this a hands on project, or strictly pen+paper?
First you would want to determine the resistance of the element. Note that the element may or may not be ohmic over the range of currents you are considering. If you have the element in front of you, hook up an ammeter and take some data...
Is it not enough to show that electrons participate in gravitational attraction, perhaps some simple F=qE=mg levitating electron in electric field Millikan-like experiment? You now know electrons feel gravity, so they should feel each other.
Directly measuring a single electron-electron...
I would say the buoyant force is simply the force due to the displacement of water, Fb= +pAyg. Since you mention that the cube floats, this buoyant force must be opposing gravity, Fg= -mg.
To double check your calculations, you might consider the equilibrium situation. When the cube is...
It looks like you are using the correct formula. The p in your formula actually is the greek letter, 'rho' which stands for density.
Keep in mind that if the cube has a mass associated with it, then the buoyant force isn't the only force which needs to be considered.
You're also right...