Two spheres of same metal have radii a and b . They have been...

Since both the metal spheres are connected to the same conducting wire, both of them will be having same charge on them. Let the charge on each of them be $q$. Then, the electric field intensities are given by, $$\begin{aligned}& E_a=\frac{k q}{a^2}, \quadE_b=\frac{k q}{b^2}\\ & \therefore \frac{E_a}{E_b}=\frac{b^2}{a^2} \end{aligned}$$