In a region, electric field varies as $E = 2x^2 -4$ where $x$ is the distance in metre from origin along $x-$ axis. A positive charge of $1\,\mu C$ is released with minimum velocity from infinity for crossing the origin, then
Medium
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For minimum kinetic energy, the velocity of the point charge will be zero at the point where electric field is zero. Let at the point $\mathrm{x}=\mathrm{x}_{0},$ the electric field is zero, then
${\rm{E}} = {\left( {2{{\rm{x}}^2} - 4} \right)_{x = {x_0}}} = 0$
$2 \mathrm{x}_{0}^{2}-4=0$ or $\mathrm{x}_{0}=\sqrt{2} \mathrm{\,m}$
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