A) \[\left( 63\hat{i}-27\hat{i} \right)\times {{10}^{2}}\]
B) \[\left( -\,63\hat{i}+27\hat{i} \right)\times {{10}^{2}}\]
C) \[\left( 81\hat{i}-81\hat{i} \right)\times {{10}^{2}}\]
D) \[\left( -\,81\hat{i}+81\hat{i} \right)\times {{10}^{2}}\]
Correct Answer: A
Solution :
| \[\vec{E}=\frac{k{{q}_{1}}}{r_{1}^{3}}{{\vec{r}}_{1}}+\frac{k{{q}_{2}}}{r_{2}^{3}}{{\vec{r}}_{2}}\] |
| \[=k\times {{10}^{-\,6}}\left[ \frac{\sqrt{10}}{10\sqrt{10}}(-\hat{i}+3\hat{j})+\frac{(-25)}{125}(-4\hat{i}+3\hat{j}) \right]\] |
| \[=(9\times {{10}^{3}})\left[ \frac{1}{10}(-\hat{i}+3)-\frac{1}{5}(-4\hat{i}+3\hat{j}) \right]\] |
| \[=(9\times {{10}^{3}})\left[ \left( -\frac{1}{10}+\frac{4}{5} \right)\hat{i}+\left( \frac{3}{10}-\frac{3}{5} \right)\hat{i} \right]\] |
| \[=9000\left( \frac{7}{10}\hat{i}-\frac{3}{10}\hat{j} \right)\] |
| \[=\left( 63\hat{i}-27\hat{j} \right)(100).\] |
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