Q51 / 75 · JEE Main 2020 (04 Sep Shift 2) · Physics

A particle of charge $q$ and mass $m$ is subjected to an electric field $E = E_{0} (1 - a x^{2})$ in the $x -$ direction, where a and $E_{0}$ are constants. Initially the particle was at rest at $x = 0$ . Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is :

Solution

$W_{ex} = ΔK K_{1} - K_{1} = 0$

$\int_{0}^{x} qEdx = 0$

$q \int_{0}^{x} E_{0} (1 - {Qx}^{2}) dx = 0$

${qE}_{0} \int_{0}^{x} (1 - {ax}^{2}) dx = 0$

$x - \frac{{ax}^{3}}{3} = 0$

$1 - \frac{{ax}^{2}}{3} = 0$

$\frac{{ax}^{2}}{3} = 1$

$x^{2} = \frac{3}{a}$

$x = \sqrt{\frac{3}{a}}$

Hence, the correct answer is option: 'C'.