Two charged conducting spheres of radii $$a$$ and $$b$$ are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:

Two conducting spheres of radii $$a$$ and $$b$$ are connected by a wire. We need the ratio of their charges. When two conductors are connected by a wire, charge flows until they reach the same electric potential.

The potential of a conducting sphere with charge $$Q$$ and radius $$r$$ is:

$$V = \frac{Q}{4\pi\varepsilon_0 r}$$

Equating the potentials of the two spheres gives $$V_1 = V_2 \implies \frac{Q_1}{4\pi\varepsilon_0 a} = \frac{Q_2}{4\pi\varepsilon_0 b},$$ which simplifies to $$\frac{Q_1}{a} = \frac{Q_2}{b} \implies \frac{Q_1}{Q_2} = \frac{a}{b}.$$

The correct answer is Option (1): $$\frac{a}{b}$$.