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184_notes:moving_q [2020/08/23 21:26] – dmcpadden | 184_notes:moving_q [2020/10/27 15:24] – dmcpadden | ||
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- | For example, consider a charge q moving in the $+\hat{x}$ direction. We want to know the magnetic field at point P that is a distance d away from the charge in the $\hat{y}$ direction at the instant the moving change is at the origin. Here, notice that must specific when we want to find the magnetic field as the change before or after that time will be at a different location -- it's moving, remember? | + | For example, consider a charge q moving in the $+\hat{x}$ direction. We want to know the magnetic field at point P, which is a distance d away from the charge in the $\hat{y}$ direction at the instant the moving change is at the origin |
$$\vec{B}=\frac{\mu_0}{4 \pi}\frac{q\vec{v}\times \vec{r}}{r^3}$$ | $$\vec{B}=\frac{\mu_0}{4 \pi}\frac{q\vec{v}\times \vec{r}}{r^3}$$ | ||
where our separation vector is $\vec{r}=d \hat{y}$ since it points from the charge to our point of interest. In this case then: | where our separation vector is $\vec{r}=d \hat{y}$ since it points from the charge to our point of interest. In this case then: |