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  4. Two charges of magnitude 5 nC and -2 nC, one placed at points (2 cm, 0, 0) and (x cm, 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

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Q. Two charges of magnitude $5\, nC$ and $-2\, nC$, one placed at points $(2\, cm, 0,\, 0)$ and $(x \,cm, 0, 0)$ in a region of space, where there is no other external field. If the electrostatic potential energy of the system is $-0.5 \, \mu J$. The value of $x$ is

Electrostatic Potential and Capacitance

Solution:

Potential energy of system
$U=\frac{1}{4\pi\varepsilon_{0}} \frac{q_{1}q_{2}}{r}$
$0.5\times10^{-6}=\frac{9\times10^{9}\times5\times10^{-9}\times\left(-2\right)\times10^{-9}}{\left(x-2\right)\times10^{-2}}$
$\Rightarrow x=20 \, cm$