The    French    scientist,    Ampere,    (1775- 1836), conducted a series of experiments on the force between current carrying conductors. He found that: force per metre of wire ( I1*I2/r) where I1 and I2  are the currents flowing in the conductors and r their distance apart. The  relationship  was  found  to  apply  to very long, thin, parallel wires.

He    concluded    that  electric currents produce  all  magnetic  fields.  It  is  now known  that  the  magnetic  properties  of solids    can  be attributed   to orbiting electrons, including a contribution from electron   spin,   both   of   which   can   be regarded as current flow (movement of charge), and that this accounts for the different magnetic properties of materials. The only    modification  to  Ampere's conclusion is that in magnetic materials the atoms align into magnetic 'domains' of macro-dimension.

Ampere also found experimentally that the magnetic field due to a current-carrying conductor falls off with distance from the wire according to 1/r, so the density of (imaginary)   flux  lines   must   show  this effect, with the number per unit area (i.e. their density) falling as 1/r.