# What happens to Earth's charge when you remove a volume of soil?

## Homework Statement

If Earth is considered to be metal sphere (radius = 6371[km]), how much charge Q must be deposited on its surface in order for an arc to be established in the air? If surface was charged to this value by removing all electrons from a volume of soil, how large would this volume be? Assume electron density of soil = 7e23[cm-3]

## Homework Equations

Coulomb's Law is the only thing that I can imagine working at the moment.
E = (1/(4∏єo)*(q/r2)*ar

## The Attempt at a Solution

If I plug in what I know in this equation, I still have the unknown electric field intensity vector and an unknown charge, which is what I'm solving for in the first part of this problem. I do not know how to implement any equation to take into account the "arc established in the air."

If someone could get me going in the right direction, perhaps the correct formula if Coulomb's Law does not apply here. Please let me know. Thanks to all help on this post!