Question

A point charge $q=100\mu C$ is located in the x-y plane at the point with position vector $\overrightarrow{r_0}=2\hat{i}+3\hat{j}+\hat{k}.$ What is the electric field vector(in kV/m) at the point with position vector $\overrightarrow{r}=8\hat{i}-5\hat{j}+\hat{k}?$

• A. $4.2\hat{i}-5.6\hat{j}$
• B. $6\hat{i}-8\hat{j}$
• C. $54\hat{i}-72\hat{j}$
• D. $5.4\hat{i}-7.2\hat{j}$

Answer 1

The correct option is C $54\hat{i}-72\hat{j}$

$q=100\mu C$

$\overrightarrow{F}=\frac{KQ(\overrightarrow{r}-\overrightarrow{r_0})}{|\overrightarrow{r}-r_0{|}^3}$

$\Rightarrow \frac{K{x}^1\times 100\times {10}^{-6}\times (6\hat{i}-5\hat{j}+\hat{k}-(2\hat{i}+3\hat{j}+\hat{k}\left)\right)}{|6\hat{i}-6\hat{j}+\hat{k}-2\hat{i}-3\hat{i}-3\hat{j}-\hat{k}{|}^3}$

$\Rightarrow \frac{K\times {10}^{-4}\times (6j-8\hat{j})}{|6\hat{j}-8\hat{j}{|}^3}$

$\Rightarrow \frac{K\times {10}^{-4}\times (6\hat{i}-8\hat{j})}{(10{)}^3}$

$\Rightarrow K\times {10}^{-7}\times (6\hat{i}-8\hat{j})$

$\Rightarrow 9\times {10}^{10}\times {10}^{-7}(6\hat{i}-8\hat{j})$

$\Rightarrow 9\times (6\hat{i}-8\hat{j})\times {10}^{-13}$

$\Rightarrow 54\hat{i}-72\hat{j}Kv/m$

Hence, $C$ is answer.