Two charges of magnitude $5 n C$ and $- 2 n C$ are placed at points $(2 c m, 0, 0)$ and $(x c m, 0, 0)$ in a region of space, where there is no other external field. If the electrostatic potential energy of the system is $- 0.5 μ J$ . The value of $x$ is (in m)

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Detailed Solution

Potential energy of the system

$U = \frac{1}{4 {πε}_{0}} \frac{q_{1} q_{2}}{r} \Rightarrow - 0.5 \times 10^{- 6} = \frac{9 \times 10^{9} \times 5 \times 10^{- 9} \times (- 2) \times 10^{- 9}}{(x - 2) \times 10^{- 2}} \Rightarrow x = 20 m$

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