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Find Earth's charge using Gauss's Law

  1. Feb 3, 2010 #1
    1. The problem statement, all variables and given/known data

    The electric field just above the surface of Earth has been measured to typically be 163 N/C pointing downward.

    What is the total charge on Earth's surface implied by this measurement?

    2. Relevant equations

    ∫EdA = Qinside/ɛo

    3. The attempt at a solution

    I solved this two ways and got the same answer, which is apparently wrong. using Gauss's Law: EA = Q/ɛo => Q=EAɛo = (-163)(4*pi*r^2)ɛo = -735.56 kC
  2. jcsd
  3. Feb 3, 2010 #2
    Earth's radius is about 6.4E6 m so squared is about 41E12 m^2.
  4. Feb 3, 2010 #3
    right so these are my numbers:


    but this produces a wrong answer (has to be within about 97% accuracy) of -735562.52C
    or -735.56 kC
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