# Biot-Savart law

Biot-Savart law
관련코스 전기역학
소분류
선행 키워드
연관 키워드

If there is a steady line current, the magnetic field due to the current is:

$\mathbf{B}(\mathbf{r})=\frac{\mu_0}{4\pi}\int\frac{Id\mathbf{s}'\times\hat{R}}{R^2}$

where $R\equiv |\mathbf{r}-\mathbf{r}'|$ and $\mu_0$ is permeability of vacuum, which is $4\pi\times 10^{-7}\textrm{N/A}^2$

### Lorentz force

$\mathbf{F} = q(\mathbf{E}+\mathbf{v}\times\mathbf{B})$

### Magnetic forces do no work

$dW_{mag} = \mathbf{F}_{mag}\cdot d\mathbf{s} = q(\mathbf{v}\times\mathbf{B})\cdot\mathbf{v}dt =$?

### Analogy in fluid dynamics

As Maxwell suggested, Biot-Savart law resembles the relationship between fluid vortex and the velocity field.