Griffiths 1.7 Find the separation vector r from the source point (2,8,7) to the field point (4,6,8). Determine its magnitude (r), and construct the unit vector r

Griffiths 1.7 Find the separation vector r from the source point (2,8,7) to the field point (4,6,8). Determine its magnitude (r), and construct the unit vector r

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Asked by 2 years ago
945 points

Griffiths 1.7 Find the separation vector $\mathbf{r}$ from the source point (2,8,7) to the field point (4,6,8). Determine its magnitude $r$, and construct the unit vector $\hat{\mathbf{r}}$

Griffiths 1
Pairoaj

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Answered by 2 years ago
945 points

$$\mathbf{r}=\text{field point - source point}=(4,6,8)-(2,8,7)=(2,-2,1)=2\hat{x}-2\hat{y}+1\hat{z}$$

$$r=\sqrt{2^2+(-2)^2+1^2}=\sqrt{9}=3$$

$$\hat{\mathbf{r}}=\frac{\mathbf{r}}{r}=\frac{2}{3}\hat{x}-\frac{2}{3}\hat{y}+\frac{1}{3}\hat{z}$$

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