As per this diagram a point charge $ + q$ is placed at the origin $O$. Work done in taking another point charge $ - Q$ from the point $A$ [co-ordinates $(0,\,a)$] to another point $B$ [co-ordinates $(a, 0)$] along the straight path $AB$ is

110-198

  • [AIPMT 2005]
  • A

    $Zero$

  • B

    $\left( {\frac{{ - qQ}}{{4\pi {\varepsilon _0}}}\frac{1}{{{a^2}}}} \right)\,\sqrt 2 a$

  • C

    $\left( {\frac{{qQ}}{{4\pi {\varepsilon _0}}}\frac{1}{{{a^2}}}} \right)\,\frac{a}{{\sqrt 2 }}$

  • D

    $\left( {\frac{{qQ}}{{4\pi {\varepsilon _0}}}\frac{1}{{{a^2}}}} \right)\,\sqrt 2 a$

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  • [IIT 2022]

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.....$cm$