Two charges 2 $μ$ C and 1 $μ$ C are placed at a distance of 10 cm. The position of third charge from 2 C $μ$ between them so that it does not experience any force

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5.858 cm

7 cm

8 cm

2 cm

answer is C.

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Detailed Solution

$\begin{aligned} \Rightarrow \frac{k (1 \times 10^{- 6}) q}{(10 - x)^{2}} = \frac{(2 \times 10^{- 6}) q}{x^{2}} \\ \Rightarrow \frac{1}{10 - x} = \frac{\sqrt{2}}{x} \\ \Rightarrow x = 10 \sqrt{2} - x \sqrt{2} \\ \Rightarrow x (1 + \sqrt{2}) = 10 \sqrt{2} \\ \Rightarrow x = \frac{10 \sqrt{2}}{1 + \sqrt{2}} \\ \Rightarrow x = \frac{14.14}{2.414} \\ \Rightarrow x = 5.857 cm \end{aligned}$