Number of free conduction electrons in a segment of wire

[nDever]

I've written a calculator that computes the number of conduction electrons in a segment of wire with a specific gauge. For a 1 ft segment of 24awg copper wire, this is what it prints out.

AWG [0 - 36]? 24
Wire length (mm) (0 - inf)? 304.8
AWG 24
radius: 0.255 mm dia: 0.511 mm area: 0.205 mm^2
volume: 62.402 mm^3
mass: 0.559 g
moles: 0.008799 mol
atoms: 5.299E+21 atom
free elec: 5.299E+21 elec
free charge: -8.488282E+02 C

I'm taking copper to have a molar mass of 63.546 g/mol, density of 8.96 g/cm^3, and offers 1 free electron/atom for conduction.

The process is basically:
1. Determine the volume of the segment
2. Using density and volume, get the mass of the segment
3. From mass and molar mass, get the number of moles
4. From moles and Avogadro's number, compute the # of atoms

Using the elementary charge, I determine the free charge.

I've done this same type of calculation by hand, and got basically the same results with some rounding errors.

Does this result make sense? -848 coulombs of charge seems too high...

 

[kuruman]

Does this result make sense? -848 coulombs of charge seems too high...

Why? One Coulomb may be a lot of charge but Avogadro's number is a humongous number of atoms.

Here is a sobering thought. If you had Avogadro's number grains of rice and you fed the entire population on Earth (7 billion) only rice assuming a diet of 2000 Calories/day, how long would your rice supply last? Answer: 80,000 years.

 

[tech99]

The charge is enormous. That is why the slightest movement of the charge results in a strong magnetic field and radiation.