Consider two charged metallic spheres S_1 and S_2 of radii R_1 and R_2, respectively. The electric fields E_1 (on S_1 ) and E_2 (on S_2 ) on their…

Consider two charged metallic spheres $\displaystyle \mathrm{S}_1$ and $\displaystyle \mathrm{S}_2$ of radii $\displaystyle \mathrm{R}_1$ and $\displaystyle \mathrm{R}_2$, respectively. The electric fields $\displaystyle \mathrm{E}_1$ (on $\displaystyle \mathrm{S}_1$ ) and $\displaystyle \mathrm{E}_2$ (on $\displaystyle \mathrm{S}_2$ ) on their surfaces are such that $\displaystyle \mathrm{E}_1 / \mathrm{E}_2=\mathrm{R}_1 / \mathrm{R}_2$. Then the ratio $\displaystyle \mathrm{V}_1$ (on $\displaystyle \mathrm{S}_1$ )/ $\displaystyle \mathrm{V}_2$ (on $\displaystyle \mathrm{S}_2$ ) of the electrostatic potentials on each sphere is :