As electric potential of spheres are same,

                                   ${\mathrm{V}}_{\mathrm{A}}={\mathrm{V}}_{\mathrm{B}}$

$\Rightarrow {\mathrm{E}}_{\mathrm{A}}·\mathrm{a}={\mathrm{E}}_{\mathrm{B}}·\mathrm{b}$

$\therefore \frac{{\mathrm{\sigma }}_{\mathrm{A}}\mathrm{a}}{{\mathrm{\epsilon }}_0}=\frac{{\mathrm{\sigma }}_{\mathrm{B}}\mathrm{b}}{{\mathrm{\epsilon }}_0} \text{ or }\frac{{\mathrm{\sigma }}_{\mathrm{A}}}{{\mathrm{\sigma }}_{\mathrm{B}}}=\frac{\mathrm{b}}{\mathrm{a}}$