Question

A charged particle $q_{1}$ is at position $\left(2 , - 1,3\right)$ .The electrostatic force on another charge particle $q_{2}$ at $\left(0,0 , 0\right)$ is

• A. $\frac{q_{1} q_{2}}{56 \pi \left(\epsilon \right)_{0}}\left(2 \hat{i} - \hat{j} + 3 \hat{k}\right)$
• B. $\frac{q_{1} q_{2}}{56 \sqrt{14} \left(\epsilon \right)_{0}}\left(2 \hat{i} - \hat{j} - 3 \hat{k}\right)$
• C. $\frac{q_{1} q_{2}}{56 \pi \left(\epsilon \right)_{0}}\left(\hat{i} - 2 \hat{j} - 3 \hat{k}\right)$
• D. $\frac{q_{1} q_{2}}{56 \sqrt{14} \pi \left(\epsilon \right)_{0}}\left( 2 \hat{i} - \hat{j} +3 \hat{k}\right)$

Answer 1

Answer: (D)

$\mathrm{A}\left(q_1\right) \rightarrow(2,-1,3) $
$\mathrm{B}\left(q_2\right) \rightarrow(0,0,0) $
$\vec{F}_{\mathrm{BA}}=\frac{k q_{\mathrm{A}} q_{\mathrm{B}}}{\mid \overrightarrow{r_{\mathrm{B}}}-\overrightarrow{r_{\mathrm{A}}}}\left(\overrightarrow{r_{\mathrm{B}}}-\overrightarrow{r_{\mathrm{A}}}\right)$
$r_{\mathrm{A}}=2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+3 \hat{\mathrm{k}} ; \vec{r}_{\mathrm{B}}=0$
Putting all the values in the formula,
We get $\vec{F}_{\mathrm{BA}}=\frac{q_1 q_2}{56 \sqrt{14} \pi \varepsilon_0}(-2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-3 \hat{\mathrm{k}})$