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184_notes:pc_efield [2021/01/25 01:50] – bartonmo | 184_notes:pc_efield [2021/01/26 18:27] – [Electric Field Vectors] bartonmo | ||
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==== Electric Field Vectors ==== | ==== Electric Field Vectors ==== | ||
- | [{{ 184_notes:efieldvectora.png? | + | [{{ :184_notes:efieldvectora_new.png? |
- | To understand the electric field around a point charge (or any other distribution of charge), we will often draw vectors around the charge called " | + | To understand the electric field around a point charge (or any other distribution of charge), we will often draw vectors around the charge called " |
- | For a positive point charge Q, consider Points A-D, each a distance d (shown in red) from the charge. To draw the electric field vectors around this charge, we need to find the magnitude **//and//** direction of the electric field at each point. Starting with the electric field equation, we can find the electric field for Point A. We already know that the charge is Q, so we have: | + | For a positive point charge Q, consider Points A-D, each a distance d from the charge. To draw the electric field vectors around this charge, we need to find the magnitude **//and//** direction of the electric field at each point. Starting with the electric field equation, we can find the electric field for Point A. We already know that the charge is Q, so we have: |
$$\vec{E_A} = \frac{1}{4 \pi\epsilon_0}\frac{Q}{r_A^2} \hat{r_A}$$ | $$\vec{E_A} = \frac{1}{4 \pi\epsilon_0}\frac{Q}{r_A^2} \hat{r_A}$$ | ||
- | All we need now is to find the separation vector $\vec{r_A}$, | + | All we need now is to find the separation vector $\vec{r_A}$, |
$$r_A=|\vec{r_A}|=\sqrt{r_{Ax}^2+r_{Ay}^2+r_{Az}^2}=\sqrt{0^2+d^2+0^2}$$ | $$r_A=|\vec{r_A}|=\sqrt{r_{Ax}^2+r_{Ay}^2+r_{Az}^2}=\sqrt{0^2+d^2+0^2}$$ | ||
$$r_A=d$$ | $$r_A=d$$ |