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

  1. Sep 23, 2010 #1
    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. jcsd
  3. Sep 23, 2010 #2


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    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.
  4. Sep 23, 2010 #3
    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?
  5. Sep 24, 2010 #4


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    Looks fine except for the weight of the Earth. The mass of the Earth is 6x1024 kg.
  6. Apr 20, 2012 #5
    Please advise me how to cal the weight of the Earth?? Is it related to the mass of the Earth about 6 x 10^24kg?? Thanks!
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