Final answer:
The correct answer is that the product of the charge and the radius for both spheres is equal when they are connected by a wire, meaning qR = Qr.
Step-by-step explanation:
When two conducting spheres of radii r and R, with charges q and Q respectively, are connected by a conducting wire, the end state must be that both spheres are at the same electrical potential because the system reaches equilibrium. Since they are now an equipotential system, the voltage (V) across each must be the same. By definition of potential (V), which is V = k * q / r for a sphere of charge q and radius r, where k is Coulomb's constant, the potentials for the two spheres must satisfy Vr = k * q / r and VR = k * Q / R.
Setting these equal to each other because the spheres are at the same potential, we get k * q / r = k * Q / R. Solving this equation for the charges' relationship gives qR = Qr, hence the correct answer is option B: qR = Qr.