Find Earth's charge using Gauss's Law

AI Thread Summary
The discussion focuses on calculating Earth's total surface charge using Gauss's Law, given an electric field of 163 N/C directed downward. The user attempted to apply the formula Q = EAε₀, substituting the electric field and Earth's radius to find a charge of approximately -735.56 kC. However, the result was deemed incorrect, as it did not meet the required accuracy threshold. The calculations involved using Earth's radius to determine the surface area, but the final answer was still off. The thread highlights the challenges in applying Gauss's Law accurately in this context.
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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
 
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ndoc said:

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.
 
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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