Question

A point charge$(+10\text{nC})$ is kept at point $P(1,2,3)$ and a test charge is kept at point $Q(3,4,5)$. Find the electric field experienced by the test charge.
$[$Assume distances in metre$]$

• A. $2.2(\hat{i}+\hat{j}+\hat{k})\text{N/C}$
• B. $3.3(\hat{i}+\hat{j}+\hat{k})\text{N/C}$
• C. $4.4(\hat{i}+\hat{j}+\hat{k})\text{N/C}$
• D. $5.5(\hat{i}+\hat{j}+\hat{k})\text{N/C}$

Answer 1

The correct option is C $4.4(\hat{i}+\hat{j}+\hat{k})\text{N/C}$

Given:
Charge, $q=+10\text{nC}$
Point, $P(1,2,3)$
Point, $Q(3,4,5)$
So position of test charge wrt $P$ can be represented as $\overrightarrow{r}=(3\hat{i}+4\hat{j}+5\hat{k})-(1\hat{i}+2\hat{j}+3\hat{k})$
$\Rightarrow \overrightarrow{r}=2\hat{i}+2\hat{j}+2\hat{k}$
Further, $r=\sqrt{2^2+2^2+2^2}=2\sqrt{3}\text{m}$

We know that,
$\overrightarrow{E}=\frac{kq}{r^3}\overrightarrow{r}$
On putting values,
$\overrightarrow{E}=\frac{9\times {10}^9\times 10\times {10}^{-9}}{(2\sqrt{3}{)}^3}\times (2\hat{i}+2\hat{j}+2\hat{k})$
$\Rightarrow \overrightarrow{E}=2.2(2\hat{i}+2\hat{j}+2\hat{k})$
$\Rightarrow \overrightarrow{E}=4.4(\hat{i}+\hat{j}+\hat{k})\text{N/C}$