How many Amp turns around the Earth for this flux density?

[Clark Magnuson]

Someone is asking me how much current in a loop of wire the diameter of the Earth to make the same level of magnetism the Earth has?

I hope I am asking this correctly.
TIA
Clark

 

[jrmichler]

It's been almost 20 years since I calculated an electromagnet, but I'll try anyway.

Earth's magnetic field strength is about 0.5 Gauss = 0.5E-4 Tesla
Length = 13,000,000 meters (diameter of Earth)
Mu = 4 PI E-7 Weber/ampere-meter (permeability of free space, might be way off considering the iron and nickel in Earth's core)

NI = 0.5E-4 X 13E6 / 4 PI E-7 = 500,000,000 ampere-turns. I welcome any confirmation and/or correction.

 

[Tom.G]

Let's see how to build a coil to cancel that field. Since I don't expect an implementation. I'll be rounding off values here.

Choose AWG #0 Copper wire with a diameter over insulation of 0.5inch.

Dia. 0.5in. = 24 Turns/Ft. = 126 720 Turns/mile
Res Ohm/1000Ft = 0.1 Ohms = 5.28 0.528 Ohms/Mile
Weight = 3.13ft/pound = 5280/3.13 = 1687lb/mi
Current rating 150A

5E8 Ampere-Turns needed
Earth Circumference = 24000 Miles

5E8AT/150A = 3.3E6 Turns * 24000 = 8E10 miles of wire
3.3E6/126720 Turns per mile = one-layer winding 26.3 Miles wide

3.3E6 Turns * 24000 = 8E10 miles of wire
8E10 * 16871lb/mi = 1.35E15 pounds of wire

8E10 miles * 5.28 0.528 Ohms per mile = 4.224E11 10 Ohms
150A * 4.224E11 10 = 6.3E1312 Volts to drive the coil

With 1.35E15 pounds of Copper wire needed and Global Copper production of 5E10 pounds per year, you would need 27000 years to mine the Copper.

It looks like Earth-sized Helmholtz coils won't be in our lifetime.

Cheers,
Tom

 

[jrmichler]

Clearly, we now need a power calculation.

6.3E13 volts X 150 amps = 9.45E15 watts = 9,450,000 GW.
Total world electrical generating capacity = 15,856 GW (https://www.cia.gov/library/publications/the-world-factbook/rankorder/2236rank.html)

The total world generating capacity is only short by a factor of 600.

 

[Tom.G]

Correction to posts #3 and #4.

...I'll be rounding off values here.

It turns out I did more than round off, I made a power-of-10 error in the resistance. That made the needed Voltage too high by a factor of 10.
My post #3 has been corrected.

Unfortunately, that also impacted @jrmichler post #4, making it too high by a factor of 10. Sorry.

Clearly, we now need a power calculation.

6.3E13 volts X 150 amps = 9.45E15 watts = 9,450,000 GW.
Total world electrical generating capacity = 15,856 GW (https://www.cia.gov/library/publications/the-world-factbook/rankorder/2236rank.html)

The total world generating capacity is only short by a factor of 600.

The updated values would be 945,000 GW and generating capacity short by a factor of 60.