Question

Find out the magnitude of electric field intensity and electric potential due to a dipole of dipole moment $\overline{P}=\hat{i}+\sqrt{3}\hat{j}$ kept at origin at following points.
(i) (2, 0, 0)
(ii) (-1, $\sqrt{3}$, 0)

Answer 1

$E=\frac{k\left|\overrightarrow{p}\right|}{{\left|z\right|}^3}\overrightarrow{z}=2\hat{i}\overrightarrow{p}=\hat{i}+\sqrt{3}\hat{j}k=9\times {10}^{9}E=\frac{9\times {10}^9\times \sqrt{10}}{8}E=35.575\times {10}^{8}V=\frac{\overrightarrow{p}.\hat{r}}{4\pi {\epsilon }_0{r}^2}\overrightarrow{r}=-\hat{i}+\sqrt{3}\hat{j}\left|\overrightarrow{r}\right|=\sqrt{1^2+3^2}\left|\overrightarrow{r}\right|=\sqrt{10}V=\frac{(\hat{i}+\sqrt{3}\hat{j}).(-\hat{i}+\sqrt{3}\hat{j})}{4\pi {\epsilon }_0\times 10}V=\frac{9\times {10}^9}{10}\times (-1+3)V=\frac{9}{5}\times {10}^{9}V=1.8\times {10}^9$