Question

A charge $q=1\mu C$ is placed at point $(1\text{m},2\text{m},2\text{m})$. Find the magnitude of electric field at point $(0\text{m},1\text{m},1\text{m})$

• A. $1\times {10}^3\text{N/C}$
• B. $2\times {10}^3\text{N/C}$
• C. $3\times {10}^3\text{N/C}$
• D. $4\times {10}^3\text{N/C}$

Answer 1

The correct option is C $3\times {10}^3\text{N/C}$

Given, $P(1\text{m},2\text{m},2\text{m})$ and $Q(0\text{m},1\text{m},1\text{m})$

So,
$|PQ|=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2+(z_2-z_1{)}^2}$
$\Rightarrow r=\sqrt{1^2+1^2+1^2}=\sqrt{3}\text{m}$
Further magnitude of electric field is $E=\frac{kq}{r^2}$
$\Rightarrow E=\frac{9\times {10}^9\times 1\times {10}^{-6}}{(\sqrt{3}{)}^2}$
$\Rightarrow E=3\times {10}^3\text{N/C}$

$\begin{array}{c}\text{Why this question ?}\\ \text{Concept - For given two points}P(x_1,y_1,z_1)\text{and}\\ Q(x_2,y_2,z_2)\text{distance between them is given by}PQ=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2+(z_2-z_1{)}^2}\end{array}$