Relative positioning system using Electromagnetic field from a wire
The datasheet for that sensor says it triggers at 200 Gauss and releases at about 130 Gauss. That is 0.02 Tesla and 0.013 Tesla.

The equation for magnetic field strength from a straight wire carrying current is:


From Physics Central

where \$u_0 = 4\pi \times 10^{-7} \$ Tesla/m/amp

I get 1000A before your chosen sensor will trip at 1cm.