Question

Is there any way to calculate the total charge of the earth?(Theoretically or experimentally)
I know the capacitance of the earth, but have no idea what to do with it.

Answer 1

perhaps my measuring the force on charged object at space.

Answer 2

That's a nice idea. I see values of charge of the earth on the net, but I wonder how they have got that!

Answer 3

Gauss law .. perhaps.

Answer 4

http://www.rheintech.com/blog/archives/1025

Answer 5

i know the sun has quite a charge ,

Answer 6

If we assume that the electric field at the surface of Earth is E, according to Gauss law we have:\[\epsilon _{0} \int\limits E.dA=q \rightarrow \epsilon _{0}(E.dA)=dq=\sigma dA\]after simplification we have:\[\sigma=\epsilon_{0}E\]the whole charge is:\[Q=\sigma(4\pi R_{E}^2)=4\pi \epsilon_{0}ER_{E}^2\]
we know that at a fine day E is about 150 N/C. now we can calculate the total charge:
\[Q=(4)(3.141)(8.854 \times 10^{-12})(150)(6.37 \times 10^6)^2=6.77 \times 10^5 C \approx 6.8 \times 10^5 C\]

Answer 7

Oh my God! how stupid I am! there is a very simple way too: "the magnitude of the electric field outside a uniformly charged sphere is the same as if all the charge were concentrated at the center." so we have:\[E=Q/4\pi \epsilon_{0} R_{E}^2 \rightarrow Q=4\pi \epsilon_{0}E R_{E}^2\]

Answer 8

because they are different values declared for electric field at the surface of earth we may find different numbers for Q. but they are similar enough to make a good approximation.
the values are between 100 and 150 N/C. so the amount of charge might be between 680KC and 450KC. hence, the best answer we could define is about:\[5.6 \pm 1.1 \times 10^5C\]

Answer 9

@ParsaN, I think you have considered the earth to be a hollow sphere. But it is a solid sphere in fact. So surface charge density should be replaced by volume density.

Answer 10

the Earth is firmly conductor, hence the charge spreads on its surface.