How Can I Calculate the Volume of Soil with a Given Charge?

[satchmo05]

Homework Statement

If the Earth's surface was charged to Q_TOTAL = 13548.3 [C] by removing all of the electrons from a volume of soil, how large would this volume be? Assume electron density of soil = 7e²³ [cm^-3].

Homework Equations

Volumetric charge density p_v = Q_TOTAL/volume of soil.

Electron density is = # of electrons per unit volume.

The Attempt at a Solution

By rearranging the volumetric charge density formula, I can gather that Q_TOTAL / p_v. Rearranging the second formula, I can get volume equal to #electrons/electron density. In a general sense, density is equal to mass/volume. I could solve for volume easily here, knowing the mass of an electron. But then, how is charge involved? How do I get the volume of soil, given the amount of charge that was removed from this volume?

Thank you for the help!

 

[ehild]

No mass is involved in this problem. You have charge, charged particles (electrons) and their density. You know the charge of an electron. Knowing the electron density (number of electrons in 1 cm^-3), calculate the charge density. From the total charge and charge density, you get the volume.

ehild