Two charged conducting spheres S_1 and S_2 of radii 8 cm and 18 cm...

When two conducting spheres are connected by a wire, charge flows until their potentials become equal.

$V_1 = V_2$

$\dfrac{k Q_1}{R_1} = \dfrac{k Q_2}{R_2}$

The electric field on the surface of a conducting sphere is given by $E = \dfrac{k Q}{R^2}$, which can be written as $E = \dfrac{V}{R}$.

Since $V_1 = V_2$, we have:

$E_{S_1} R_1 = E_{S_2} R_2$

$\dfrac{E_{S_1}}{E_{S_2}} = \dfrac{R_2}{R_1}$

Given $R_1 = 8$ cm and $R_2 = 18$ cm:

$\dfrac{E_{S_1}}{E_{S_2}} = \dfrac{18}{8} = \dfrac{9}{4}$

Answer: $\dfrac{9}{4}$