A 60 kg person is standing on a thin, conductive disk (the person is wearing thick rubber shoes, so the person is electrically separate from the conductive disk). The disk is connected to a VGG and the person places a hand on an identical, but separate VGG. If each of the VGG are activated (turned on) at the same instant and both remove electrons at a rate 500 determine: (a) the amount of time the person would have to hold onto the VGG to float 1 mm above the conductive disk; (b) the amount of mass that the person will gain or lose during this time. Did the person gain or lose this mass

a)   t = 3.2 10¹⁴ s , b)    Δm = 1,456 10⁻¹³ kg, mass decreases

Explanation:

In this exercise the removed electrons leave a positive charge on each disk, as the two charges are of the same sign they repel each other, so using Newton's equilibrium equation

                    –W = 0

                    F_{e} = W = mg

Electric force is

                    F_{e} = k q₁ q₂ / r²

Since the two generators remove 500 e/s, q₁ = q₂ = q

                    F_{e} = k q² / r²

                   k q² / r² = m g

                   q = √ m g r²/ k

                   q = √ (60 9.8 0.001² / 8.99 10⁹)

                   q = √ 6.54 10⁻⁴

                   q = 2.56 10⁻² C

This is the charge on each disk

                  q = # _electron  e

                  # _electron = q / e

                  # _electron = 2.56 10⁻² / 1.6 10⁻¹⁹

                  # _electron = 1.6 10¹⁷  electrons

Let's use a rule of proportions to find the accumulation time, if the rate is 500 e/s

                  t = 1.6 10¹⁷  1/500

                  t = 3.2 10¹⁴ s

b) how electrons are losing their mass decreases

                 Δm = me # _electron

                 Δm = 9.1 10⁻³¹  1.6 10¹⁷

                 Δm = 1,456 10⁻¹³ kg

the force on the thing and the distance the force moves the thing

the minimum amperage that the current in this wire would have to have so that its weight is completely supported by the magnetic force due to earth's field, assuming that no other forces except gravity act on it