A) \[30cm\]
B) \[6m\]
C) \[5cm\]
D) \[3m\]
Correct Answer: D
Solution :
Given : (b ? a) = 1 ´ 10?3 m ..... (i) and \[C=4\pi {{\varepsilon }_{0}}\left( \frac{ab}{b-a} \right)=1\times {{10}^{-6}}\] Þ \[1\times {{10}^{-6}}=\frac{1}{9\times {{10}^{9}}}\left( \frac{ab}{{{10}^{-3}}} \right)\] Þ \[ab=9\] ..... (ii) From equations (i) and (ii) \[b-\frac{9}{b}=\frac{1}{1000}\] Þ 1000 b2 ? b ? 9000 = 0 Þ \[b=\frac{1\pm \sqrt{{{(-1)}^{2}}\,-\,4(1000)\,(-\,9000)}}{2\times 1000}\] {Solving of quadratic equation} Þ \[b=\frac{1\pm \sqrt{36\times {{10}^{6}}}}{2000}\approx \,\frac{\sqrt{36\times {{10}^{6}}}}{2000}=3\,m.\]You need to login to perform this action.
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