14.2.3 Current Balance

The magnetic flux density of a magnetic field can be measured by measuring the force it exerts on a current carrying conductor.

$\displaystyle \begin{aligned}{{F}_{b}}&=BIL\\B&=\frac{{{{F}_{b}}}}{{IL}}\end{aligned}$

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 F_b and the CW moment caused by W (about the razor blade pivot):

$\displaystyle \begin{aligned}{{F}_{b}}\times {{L}_{1}}&=W\times {{L}_{2}}\\BIL\times {{L}_{1}}&=W\times {{L}_{2}}\\B&=\frac{W}{{IL}}\frac{{{{L}_{2}}}}{{{{L}_{1}}}}\end{aligned}$