An electric charge 2 x 10^-8 C is placed at the point (1, 2, 4). At the point (3, 2, 1), the electric

${\overrightarrow{\mathrm{r}}}_{\mathrm{P}}=\hat{\mathrm{i}}+2\hat{\mathrm{j}}+4\hat{\mathrm{k}}; {\overrightarrow{\mathrm{r}}}_{\mathrm{q}}=3\hat{\mathrm{i}}+2\hat{\mathrm{j}}+\hat{\mathrm{k}}$

$\left|{\overrightarrow{\mathrm{r}}}_{\mathrm{q}}-{\overrightarrow{\mathrm{r}}}_{\mathrm{P}}\right|=\sqrt{\left[(2{)}^2+(-3{)}^2\right]}=\sqrt{13}$

As $\mathrm{q}=2\times {10}^{-8}\mathrm{C}$

$\mathrm{V}=\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{\mathrm{q}}{\left|{\overrightarrow{\mathrm{r}}}_{\mathrm{q}}-{\overrightarrow{\mathrm{r}}}_{\mathrm{p}}\right|}$

$=\frac{9\times {10}^9\times 2\times {10}^{-8}}{\sqrt{13}}=49.9\mathrm{V}$

$\overrightarrow{\mathrm{E}}=\frac{1}{4{\mathrm{\pi \epsilon }}_0{\left|{\overrightarrow{\mathrm{r}}}_{\mathrm{q}}-{\overrightarrow{\mathrm{r}}}_{\mathrm{P}}\right|}^2}\frac{\left({\overrightarrow{\mathrm{r}}}_{\mathrm{q}}-{\overrightarrow{\mathrm{r}}}_{\mathrm{P}}\right)}{\left|{\overrightarrow{\mathrm{r}}}_{\mathrm{q}}-{\overrightarrow{\mathrm{r}}}_{\mathrm{P}}\right|}$

$=\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{\mathrm{q}}{{\left|{\overrightarrow{\mathrm{r}}}_{\mathrm{q}}-{\overrightarrow{\mathrm{r}}}_{\mathrm{p}}\right|}^3}(2\hat{\mathrm{i}}-3\hat{\mathrm{k}})$

(By filling a dielectric of dielectric constant K, electric field gets decreased as $\mathrm{E}={\mathrm{E}}_0/\mathrm{K}\text{ and }\mathrm{K}>1$.)