A) \[\frac{2}{\sqrt{3}}\]
B) \[\frac{2(\hat{i}+\hat{j}+\hat{k})}{3}\]
C) \[\frac{2}{8(\hat{i}+\hat{j}+\hat{k})}\]
D) \[\frac{3}{2(\hat{i}+\hat{j}+\hat{k})}\]
Correct Answer: B
Solution :
\[V=\frac{3}{{{r}^{2}}}\] \[\overrightarrow{E}=-\left( \frac{dV}{dr} \right)\hat{r}=-\frac{\partial }{\partial r}\left[ \frac{3}{{{r}^{2}}} \right]\hat{r}=\frac{6}{{{r}^{4}}}\overrightarrow{r}\] \[E=6\frac{(\hat{i}+\hat{j}+\hat{k})}{{{(\sqrt{3})}^{4}}}=\left( \frac{2}{3} \right)(\hat{i}+\hat{j}+\hat{k})\]
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