How many electrons must be moved from the metal plate to you in order for you to hang suspended in the air?

Question

As a science project, you've invented an "electron pump" that moves electrons from one object to another. To demonstrate your invention, you bolt a small metal plate to the ceiling, connect the pump between the metal plate and yourself, and start pumping electrons from the metal plate to you. How many electrons must be moved from the metal plate to you in order for you to hang suspended in the air 2.00 m below the ceiling? Your mass is 70.0 kg.

Answer 1

I suppose you floating parallel to the ceiling;    

♣ your weight is F=m*g = 70.0*9.8 N;

♦ Coulomb’s force on you is

F=q*q/(4π*ε0*r^2), where ε0=8.854e-12, r=2m;

♠ you-are-balanced means F=F; m*g = q^2/(4π*ε0*r^2), hence charge on you (as well as on the plate) is

q=√(mg*4π*ε0*r^2) = √(70*9.8* 4*3.1416*8.854e-12) *2 =0.000552544 C;

number of electrons is n=q/e, where e=1.602e-19 C is charge of electron;

n= 0.000552544 /1.602e-19 =3.45e15;