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

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2. Electric Potential and Capacitance

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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.....$cm$

A

$20$

B

$80$

C

$4$

D

$16$

Solution

Potential energy of system

$\mathrm{U}=\frac{1}{4 \pi \varepsilon_{0}} \frac{\mathrm{q}_{1} \mathrm{q}_{2}}{\mathrm{r}}$

$0.5 \times 10^{-6}=\frac{9 \times 10^{9} \times 5 \times 10^{-9} \times(-2) \times 10^{-9}}{(\mathrm{x}-2) \times 10^{-2}}$

$\Rightarrow \mathrm{x}=20 \mathrm{\,cm}$

Standard 12

Physics

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(IIT-2011)