# Current Loop equivalent to Earth's Magnetic Field

1. Jan 17, 2014

### .Scott

I'm trying to get a feel for the overall magnitude of the Earth's magnetic field.

If I placed a superconducting belt around the Earth magnetic equator, how much current would that loop have to carry to approximate the Earth magnetic field?

Currently, the field at the equator is about 31 microT and at 50 degrees latitude is about 58 microT.

If I replace the Earth with a vacuum, it looks like I would need on the order of 20MA - but I have no confidence in that estimate. It looks to me as though the Earth's iron content might bring this number down.

2. Jan 17, 2014

### Bobbywhy

3. Jan 17, 2014

### .Scott

That all very incredibly detailed - but I would settle for and answer that's off by a factor of 2.
I have the basic data and the B=uI/2R formula (for the center of a current ring). What I don't have is any experience calculating magnetic fields directly from currents - so I am very uncertain of my computations.

Also, the B=uI/2R is for the center of a current ring, not on the surface of a sphere girdled by a current ring - so I don't have a direct comparison. The B=uI/2R also assumes a constant permeability (u) which is not the case of a solid sphere hanging in a vacuum.