Two uniformly charged spherical conductors A and B of radii 5mm and...

When two conductors are connected by a conducting wire, their potentials become equal. Therefore, ${V}_{A} = {V}_{B}$

The potential of a spherical conductor is given by, $V = \dfrac{kQ}{R}$

$⇒ \dfrac{k{Q}_{A}}{{R}_{A}} = \dfrac{k{Q}_{B}}{{R}_{B}}$

$⇒ Q ∝ R$

Now the electric field near the surface of the conductor will be, $E = \dfrac{kQ}{{R}^{2}}$

$⇒ \dfrac{{E}_{A}}{{E}_{B}} = \dfrac{k{Q}_{A}{R}_{A}^{2}}{k{Q}_{B}{R}_{B}^{2}} = \dfrac{{R}_{B}}{{R}_{A}}$

$⇒ \dfrac{{E}_{A}}{{E}_{B}} = \dfrac{10}{5} = \dfrac{2}{1}$