Consider a solid insulating sphere of radius $R$ with charge density varying as $\rho = \rho _0r^2$ ($\rho _0$ is a constant and $r$ is measure from centre). Consider two points $A$ and $B$ at distance $x$ and $y$ respectively $(x < R, y > R)$ from the centre. If magnitudes of electric fields at points $A$ and $B$ are equal, then 

  • A

    ${x^2}y = {R^3}$

  • B

    ${x^3}y^2 = {R^5}$

  • C

    ${x^2}y^3 = {R^5}$

  • D

    $\frac{{{x^4}}}{y} = {R^5}$

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