In principle, the Biot-Savart law can be used to calculate the magnetic field of any current distribution. In practice, the integrals are difficult to evaluate for anything other than very simple situations. We faced a similar situation for calculating electric fields, but we discovered an alternative method—Gauss’s law—for calculating the electric field of charge distributions with a high degree of symmetry.
Likewise, there’s an alternative method, called Ampère’s law, for calculating the magnetic fields of current distributions with a high degree of symmetry. Whereas Gauss’s law is written in terms of a surface integral, Ampère’s law is based on the mathematical procedure called a line integral.