Biot-Savart Law

#Physics

$\displaystyle \vec{B}(r)=\frac{{\mu}{0}}{4\pi}\int \frac{\vec{I}\times \vec{\mathscr{r}}}{\mathscr{r}^{2}} , \mathrm{d}l'=\frac{{\mu}{0}I}{4\pi}\int \frac{\mathrm{d}\vec{l}' \times \hat{\mathscr{r}}}{\mathscr{r}^{2}}$

• The magnetic field a distance $\displaystyle r$ from a steady current distribution
• $\displaystyle {\mu}_{0}$ is the magnetic constant
• $\displaystyle \vec{I}$ is the current vector
• Analogous to Coloumb's law

$\displaystyle \vec{B}(\vec{r},t)=\frac{{\mu}_{0}}{4\pi} \frac{q}{R^{2}}(\vec{v}\times \vec{R})$

• $\displaystyle \vec{R}=\mathscr{\vec{r}}-\vec{v}t$