Two uniformly charged spherical conductors $A$ and $B$ of radii $5 mm$ and $10 mm$ are separated by a distance of $2 cm$. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surface of the sphere $A$ and $B$ will be .
JEE MAIN 2022, Medium
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$V _{ A }= V _{ B }$
$\frac{ KQ _{ A }}{ R _{ A }}=\frac{ KQ _{ B }}{ R _{ B }}$
$\frac{ Q _{ A }}{ Q _{ B }}=\frac{ R _{ A }}{ R _{ B }}=\frac{1}{2}$
$E _{ A }=\frac{ KQ _{ A }}{ R _{ A }^{2}} ; E _{ B }=\frac{ KQ _{ B }}{ R _{ B }^{2}}$
$\frac{ E _{ A }}{ E _{ B }}=\frac{ Q _{ A }}{ Q _{ B }} \times \frac{ R _{ B }{ }^{2}}{ R _{ A }{ }^{2}}=\frac{ R _{ B }}{ R _{ A }}=\frac{2}{1}$
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