The magnetic flux density of a magnetic field can be measured by measuring the force it exerts on a current carrying conductor.
Basically, we are going to measure the magnetic force per unit current per unit length. The setup is called a current balance.
For example (see above), to measure the magnetic field between a pair of magnadur magnets, we position side PQ of a rectangular coil perpendicularly inside the field. We then balance the coil on a pair of razor blades, like a see-saw. Next, we (1) add a weight W to the RS side of the coil, and (2) pass a current through the coil. The rheostat is adjusted until the rotational equilibrium is restored.
The magnitude of B can then be calculated by equating the ACW moment caused by Fb and the CW moment caused by W (about the razor blade pivot):