Biot-Savart Law

$\vec{B}(r)=\frac{{\mu }_0}{4\pi }\int \frac{\vec{I}\times \vec{r}}{r^2}\mathrm{d}{l}^{\prime }=\frac{{\mu }_{0}I}{4\pi }\int \frac{\mathrm{d}{\vec{l}}^{\prime }\times \hat{r}}{r^2}$

• The magnetic field a distance $r$ from a steady current distribution
• ${\mu }_0$ is the magnetic constant
• $\vec{I}$ is the current vector
• Analogous to Coloumb’s law

$\vec{B}(\vec{r},t)=\frac{{\mu }_0}{4\pi }\frac{q}{R^2}(\vec{v}\times \vec{R})$

• $\vec{R}=\vec{r}-\vec{v}t$