A wire of length $L\, (=20\, cm)$, is bent into a semicircular arc. If the two equal halves of the arc were each to be uniformly charged with charges $ \pm Q\,,\,\left[ {\left| Q \right| = {{10}^3}{\varepsilon _0}} \right]$ Coulomb where $\varepsilon _0$ is the permittivity (in $SI\, units$) of free space] the net electric field at the centre $O$ of the semicircular arc would be

822-820

  • [JEE MAIN 2015]
  • A

    $\left( {50 \times {{10}^3}\,N/C} \right)\hat j$

  • B

    $\left( {50 \times {{10}^3}\,N/C} \right)\hat i$

  • C

    $\left( {25 \times {{10}^3}\,N/C} \right)\hat j$

  • D

    $\left( {25 \times {{10}^3}\,N/C} \right)\hat i$

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