Submitted by dvorahtheexplorer t3_zhic83 in askscience
KingoPants t1_izo990t wrote
Reply to comment by MiffedMouse in What is the average voltage between Earth and outer space? by dvorahtheexplorer
Putting numbers to this:
If we approximate earth as a conductive sphere with a particular radius in a vaccuum. It's capacitance to infinity is equal to C = 4πϵ_0R.
Plugging in the radius of the earth into that you get a capacitence of Q=710 uF.
By definition of capacitence Q=CV. V=Q/C gives you the voltage.
Now for a mass (m) to gravitationationally escape earth then you need E=GMm/R energy where M is earth's mass and R is earth's radius.
Now if you set that energy to E>V*q where q is the charge of that charged mass it is energetic favourable for that mass to escape earth.
Put together you get the final big equation out:
Q = GM4πϵ_0*(m/q). This is how much charge you need on the surface of earth to start to fling stuff off earth.
If you want to fling out electrons then it turns out you need a net negative charge of 252 nano culombs.
To fling out a hydrogen ion / a proton you would need 463 uC. To fling out an alpha particle would take 920 uC.
It's not a ton really. Considering how big the earth is.
[deleted] t1_izpfivz wrote
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