Question

Nobel laureate Richard Feynman (1918-1988) once said that if two persons stood at arm's length from each other and each person had 1% more electrons than protons, the force of repulsion between them would be enough to lift a "weight" equal to that of the entire Earth. Carry out an order-of-magnitude calculation to substantiate this assertion.
F~10:_____________N

Answer 1

Assuming mass of avg person = m = 75 kg

Suppose there is equal number of proton, neutron and electron in human body.

Now electron of mass is negligible compare to mass of proton and neutron

Then number of protons in human body = N = (m/2)/mp

mp = mass of proton = 1.67*10^-27

Now given that there is 1% more electron than proton, So

Number of electron = N*0.01

q = m*0.01*qe/(2*mp)

q = 75*0.01*1.6*10^-19/(2*1.67*10^-27) = 35928143.7

Now electrostatic force is given by:

F = kq^2/r^2

r = arm's length = 1 m

F = 9*10^9*35928143.7^2/1^2

F = 1.16*10^25 N

Now weight of earth is

F = m*g = 5.98*10^24*9.81 = 5.86*10^25

So force is 10^25 N, which is equal to earth's weight.