# Force of Repulsion between two people with 1% more electrons than protons

1. Sep 23, 2010

### gsquare567

1. The problem statement, all variables and given/known data
Richard Feynman 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 the two people 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.

2. Relevant equations
F(elec) = k*q^2 / r^2
mass of Earth = 5.9742 × 10^24 kilograms

3. The attempt at a solution
I am stuck with the beginning; how do I know how many electrons that is? And how do I find the charge given the number of electrons?

Thanks a lot!

2. Sep 23, 2010

### kuruman

There is no specific number of protons. You have to figure out a reasonable number using reasonable assumptions. It is not 3 and it is not 1040, but something in-between. You know the mass of an average person, so how many protons is that? Like I said, make some assumptions and use the mass of a proton, which that you can look up. You can also look the charge of an electron which the same in magnitude as the charge of a proton.

3. Sep 23, 2010

### gsquare567

Ok. Amazing. Thanks for the quick reply. Here's what I've come up with:

protons:electrons ~= 1:1

average human mass ~= 6.00x10^4 g

mass of one proton is 1 amu = 1.6607x10^-24 g

mass / amu mass = #protons + #neutrons
-> 6.00x10^4g / 1.6607x10^-24g = 3.61x10^28

divide by 2 to get the # of protons
-> 3.61x10^28 / 2 = 1.80x10^28 protons

--> there are approximately 1.80x10^28 electrons in a human body

1% of that is 1.80x10^26

1 Coulomb = −6.24151 × 10^18 electrons

-> a human body with 1% more electrons than protons has a charge of...
1% of electrons in body / # electrons in Coulomb = -2.88x10^7 C

Say arms length is 1m => r^2 = 1m^2

WOW I GET IT!!!

F(elec) = k * q^2 / r^2 = (9 * 10^9 N*m^2/C^2) * (-2.88x10^7 C)^2 / 1 m^2
= 7.46 * 10^24 N

weight of earth = mg = 4*10^15 N

=> the electric force is 2*10^9 times larger than the weight of the earth (according to this approximation), so it is probably true that the repulsion of two people, each with 1% more electrons than protons, can have a force of repulsion enough to lift a weight equal to that of the entire earth.

How is that?

4. Sep 24, 2010

### kuruman

Looks fine except for the weight of the Earth. The mass of the Earth is 6x1024 kg.

5. Apr 20, 2012