Question

A point charge $q=100\mu C$ is located in the $x-y$ plane at the point with position vector ${\vec{r}}_0=2\hat{i}+3\hat{j}+\hat{k}$. What is the magnitude of electric field vector (in $kV/m$ ) at the point with position vector $\vec{r}=8\hat{i}-5\hat{j}+\hat{k}?$

Answer 1

Answer: 9

Separation between two points,
$r=\sqrt{{\left(x_1-x_2\right)}^2+{\left(y_1-y_2\right)}^2}=10m$
Now, $|\vec{E}|=\frac{1}{4\pi {\epsilon }_0}\frac{q}{r^2}$
Hence,
$E=\frac{9\times 10^9\times 100\times 10^{-6}}{100}V/m$
$=9000V/m=9kV/m$