A) \[(-81\widehat{i}\,\,+\,\,81\widehat{j})\,\,\times \,{{10}^{2}}\]
B) \[(81\widehat{i}-81\widehat{j})\times {{10}^{2}}\]
C) \[(63\widehat{i}\,\,-\,\,27\widehat{j})\,\,\times \,{{10}^{2}}\]
D) \[(-63\widehat{i}+27\widehat{j})\times {{10}^{2}}\]
Correct Answer: C
Solution :
[c] |
Electric field due to \[\sqrt{10}\,\mu C\] |
\[\left| {{E}_{1}} \right|\,\,=\,\,\frac{k\,\times \,\sqrt{10}\,\times \,{{10}^{-6}}}{10}\,\,=\,\,\frac{9\,\times \,{{10}^{3}}}{\sqrt{10}}\] |
\[{{\overrightarrow{E}}_{1\,\,}}=\,\,{{E}_{1}}\sin \theta \,i\,\,+\,\,\,{{E}_{1}}\cos \theta j\] |
\[{{\overrightarrow{E}}_{1\,\,}}=\,\,\frac{9\,\times \,{{10}^{3}}}{\sqrt{10}}\,\left[ \frac{-3}{\sqrt{10}}\,i\,+\,\,\frac{1}{\sqrt{10}}\,j \right]\,\,=\,\,9\,\times \,{{10}^{2}}\] |
\[~\left( -3i+j \right)\] |
Electric field due to \[-25\,\mu C\] charge |
\[\left| {{E}_{2}} \right|\,\,\,=\,\,\frac{K\,\,\times \,\,25\,\,\times {{10}^{-6}}}{25}\,=\,9\,\times \,{{10}^{3}}\,\] |
\[{{E}_{2}}={{E}_{2}}sin\theta i-{{E}_{2}}cos\theta j\] |
\[{{\overrightarrow{E}}_{2}}=9\,\times \,{{10}^{3}}\,\left[ \frac{4}{5}i\,\,-\,\,\frac{3}{5}\,j \right]\] |
\[=\,\,18\,\times \,{{10}^{2}}\,[4i\,-\,3j]\] |
\[\overrightarrow{{{E}_{2}}}={{\overrightarrow{E}}_{1}}+{{\overrightarrow{E}}_{2}}={{10}_{2}}[63i-27j]\] |
Option |
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