Find Earth's charge using Gauss's Law

  • Thread starter ndoc
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  • #1
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Homework Statement



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?

Homework Equations



∫EdA = Qinside/ɛo


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
 

Answers and Replies

  • #2
Spinnor
Gold Member
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Homework Statement



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?

Homework Equations



∫EdA = Qinside/ɛo


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
Earth's radius is about 6.4E6 m so squared is about 41E12 m^2.
 
  • #3
13
0
right so these are my numbers:

4*pi*(-163)*(8.85x10^-12)*(6.37x10^6)^2

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

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