I found this excellent website with published theory on tethers from JPL...

Tethers in Space (c)1989

According to the documents, bare-wire tethers with an electric current moving though the Earth's magnetic field experience a force defined by the equation:

F = I x B sin(theta)

where,
F = force in Newtons
I = current in Amps
x = length of tether in meters
B = Earth's magnetic field strength in Teslas
theta = angle of tether wrt magnetic field lines in degrees

Doing some looking around I discovered that the Earth's magnetic field at sea level has horizontal and vertical components measured to be:

Bx = 0.0000187 Teslas (at sea level)
By = 0.0000436 Teslas (at sea level)

I figure this will decrease in strength by the square of the distance from the center of the earth. So if I put the Space Elevator hub in orbit at 1950 km above the surface (10,328 km from center of earth), then these values have to be multiplied by 0.381378 to get the approximately correct values. Therefore,

Bx = 0.000007131 Teslas (at 3950 km altitude)
By = 0.000016628 Teslas (at 3950 km altitude)
B = 0.000018092 Teslas (total field at 3950 km altitude)
theta = 66.79 degrees (angle of magnetic field)

These may be average estimates because the solar wind presses against the Earth's magnetic field on the side that faces the Sun, compressing it somewhat. According to my estimate of maximum force exerted on the tether while it is pulled up through the atmosphere of 1 million Newtons, we can then say that the current through the electrodynamic stationkeeping tether multiplied by its length, must exceed:

I x = 60.14 trillion

Based on the energy loss from momentum transfer and air resistance, I estimated that the maximum power needed by the tether launch system was 2.65 gigawatts (at 100 percent efficiency). Power is defined as:

P = I V

where,
P = power in watts
I = current in amps
V = electric potential in volts

Substituting this into the previous equations and using some other basic electrical relationships it may be possible to estimate how physically large the electrodynamic tethers have to be to keep this system in orbit...

....later.