Magnetostatics

Finding magnetic fields due to current distributions - there are no discrete magnetic charges (monopoles), so the only calculations are integrations of current loops. Superposition again holds and we use the Biot-Savart Law:

$$d\vec{B}={\frac{\mu _{0}I}{4\pi }}{\frac{d\vec{l}\times \hat{r}}{r^{2}}}.$$ (2)

This is a vector equation, so we are always working with vectors. In addition a current loop is a ``continuous'' source, so we are always doing integrals. The fact that magnetostatics always involves vector integrals takes some getting used to.

 

• Sample problem: Current loop