Question

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

• A. $\frac{ q _{1} q _{2}}{56 \pi \epsilon_{0}}(2 \hat{ i }-\hat{ j }+3 \hat{ k })$
• B. $\frac{1}{4 \pi \epsilon_{0}} \frac{q_{1} q_{2}}{(\sqrt{14})^{3}}(-2 \hat{i}+\hat{j}-3 \hat{k})$
• C. $\frac{q_{1} q_{2}}{56 \pi \epsilon_{0}}(\hat{j}-2 \hat{i}-3 \hat{k})$
• D. $\frac{q_{1} q_{2}}{56 \sqrt{14} \pi \epsilon_{0}}(2 \hat{i}-\hat{j}+3 \hat{k})$

Answer 1

Answer: (D)

Position vector, $\overrightarrow{ d }$
$
\begin{array}{l}
\vec{d}=(2-0) \hat{i}-(1-0) \hat{j}+(3-0) \hat{k}=2 \hat{i}-\hat{j}+3 \hat{k} \\
d^{3}=[(2 \hat{1}-\hat{j}+3 \hat{k}) \cdot(2 \hat{\imath}-\hat{j}+3 \hat{k})]^{\frac{3}{2}} \\
d^{3}=14 \sqrt{14}
\end{array}
$
Electrostatic force F
$
\begin{array}{l}
F =\frac{1}{4 \pi \varepsilon_{0}} \frac{ q _{1} q _{2}}{ d ^{3}} \overrightarrow{ d }=\frac{ q _{1} q _{2}}{4 \pi \varepsilon_{0}} \frac{(2 \hat{ i }-\hat{ j }+3 \hat{ k })}{14 \sqrt{14}} \\
F =\frac{ q _{1} q _{2}}{56 \sqrt{14} \pi \varepsilon_{0}}(2 \hat{ i }-\hat{ j }+3 \hat{ k })
\end{array}
$