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| 184_notes:moving_q [2020/10/27 15:24] – dmcpadden | 184_notes:moving_q [2020/10/27 15:28] – 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, which is a distance d away from the charge in the $\hat{y}$ direction at the instant the moving change is at the origin (see the set up below). Here, notice that we must specific about //when// we want to find the magnetic field. Because the charge is moving, it will be at a different location at different times -- our solution is only accurate for a particular time/ | + | 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 (see the set up below). Here, notice that we must be specific about //when// we want to find the magnetic field. Because the charge is moving, it will be at a different location at different times -- our solution is only accurate for a particular time/ |
| $$\vec{B}=\frac{\mu_0}{4 \pi}\frac{q\vec{v}\times \vec{r}}{r^3}$$ | $$\vec{B}=\frac{\mu_0}{4 \pi}\frac{q\vec{v}\times \vec{r}}{r^3}$$ | ||
| 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: | ||