Biot-Savart law

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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:

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

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


Lorentz force

[math]\mathbf{F} = q(\mathbf{E}+\mathbf{v}\times\mathbf{B})[/math]

Magnetic forces do no work

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

Analogy in fluid dynamics

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