How much charge would destroy the world?

Question

Someone invents a machine that creates electrons. It takes in some electrically neutral matter, and produces electrons of equal mass.¹

Let's consider two quantities of negative charge:

$q$ is the amount of negative charge that a typical individual might reasonably want to create and use, not counting in lab experiments.

$Q$ is the amount of negative charge that if added to the Earth, would soon destroy human society as we know it. (It wouldn't necessarily kill everyone, but it would trigger a huge leap backwards.)

I'd like to keep $Q\over q$ within a few orders of magnitude of $10^{10}$. This way I can keep $q$ in the budget range of an upper-class individual, while making $Q$ too expensive to create outside a major government attempt.

What are reasonable values for $q$ and $Q$?

¹ Of course this violates the principle of conservation of charge. Some skeptics claim that the machine actually sucks the electrons from another part of the universe, but it doesn't really matter.

Answer 1

Electrons are very light. If we added about 20 billion extra electrons to the surface of the earth, the charge would repel electrons with about the same strength that gravity attracts them. Add more than that, and any extra electrons would simply float away.

Twenty billion is a minuscule number of electrons, especially spread across the entire planet.

Update with more clear explanation and more accurate numbers.

The ratio of attractive force of gravity of two protons to the repulsive force of electricity is about $10^{-38}$.

One gram of Hydrogen is one mole of Hydrogen, contains $6.02 \times 10^{23}$ Hydrogen atoms. One gram of any other substance has essentially the same combined number of protons & neutrons as one gram of Hydrogen.

The Earth weighs $6 \times 10^{27}$ grams, which corresponds to the weight of $3.6 \times 10^{51}$ protons. Thus, the gravity of the Earth exerts about as much attractive force on a proton as the electrical-repulsive force of $3.6 \times 10^{13}$ protons.

Electrons weigh about 1800 times less than protons, so the gravitational pull on an electron by the Earth is that same ratio smaller. Thus, it would only take about $2 \times 10^{10}$ electrons to repel a single electron with the same electrical force that the Earth attracts the electron with, gravitationally.

Yes, 20 billion is a truly miniscule amount, essentially undetectable. Spread out evenly over the surface of the Earth, it would be about 1 extra electron per 6 acres. Yet, this extra electric charge would be enough to cancel the gravitational pull electrons feel toward the Earth. If we added any more than that, then electrons liberated in the ionosphere would accelerate away from the Earth and be lost. Balance would quickly be restored.

Note that the gravitational (or electrical) attraction toward a point mass is the same as towards a sphere centered on that point, from anywhere outside the sphere. Likewise the attraction toward a spherical shell. Thus, electrons scattered evenly over the surface of the Earth would attract/repel anything above the surface the same as if they were at the center of the Earth.