Currents and their Magnetic Fields

Ampère's law,


relates the magnetic induction \(\mathbf{B}\left(\mathbf{r}\right)\) to the current distribution \(\mathbf{j}\left(\mathbf{r}\right)\).

In this section we will learn the basic techniques to calculate the magnetic induction for a given current distribution. We will use integral methods like the law of Biot-Savart or differential methods for certain symmetries to solve Ampère's law directly.