Acording the contraction theory it seems that the density of moving electrons with respect to each other becomes higher. That all and explains the excistings of the magnetic field. The magnetic field is a kind of derivative of the force acting between charged bodies.
The current will be dominantly determined by the supply voltage U and the resistance R; it will rise to U/R in less than 1 millisecond being self inductace L over R; the self inductance can be determined with a book, Grover Inductance Calculations. So your supply voltage is the key. I expect 0.5...
Look in my publication in Magnet analysis with a Helmholz coil set
Compter, J.C. van der Veen, J.L.F.
Page(s): 177 - 182
Digital Object Identifier : 10.1049/ip-smt:20030495
Abstract | Full Text: PDF (400KB)