Two uniformly charged spherical conductors A and B of radii 5   mm and 10   mm are separated by a…

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, $V=\frac{kQ}{R}$

$\Rightarrow \frac{k{Q}_A}{R_A}=\frac{k{Q}_B}{R_B}$

$\Rightarrow Q\propto R$

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

$\Rightarrow \frac{E_A}{E_B}=\frac{{\displaystyle \frac{k{Q}_A}{R_A^2}}}{{\displaystyle \frac{k{Q}_B}{R_B^2}}}=\frac{R_B}{R_A}$

$\Rightarrow \frac{E_A}{E_B}=\frac{10}{5}=\frac{2}{1}$