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MiffedMouse t1_iznvgqe wrote

It will be close to 0. Charge imbalances create very strong forces to rebalance the charge. Space also isn’t completely empty, but it is filled with charged particles that will quickly move to rebalance any charge. This is especially true around earth, where we sit in the solar wind (the stream of charged particles coming from the sun).

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KingoPants t1_izo990t wrote

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.

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valdocs_user t1_izo420b wrote

But could the solar wind itself carry or deposit a charge imbalance? For example because protons and electrons have different masses.

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PatrickKieliszek t1_izo5c6g wrote

The solar wind is full of both positively charged hydrogen and free electrons.

The Earth's magnetic field captures more electrons than protons because the protons are more massive.

Eventually the net negative charge of the earth is enough to balance out the effect of the magnetic field and the rate of capture becomes even.

This causes the earth as a whole to have a slight negative charge.

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smnms t1_izo4h64 wrote

Not on the long run. If solar wind carried away from the sun more positive then negative charges, the sun would build up a positive charge, and this would pull back all the negatively charged particles.

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