The setup is as below:
The two conducting spheres, of radii $r_1$ and $r_2$ have charges $Q_1$ and $Q_2$. The distance between their centers is AB. BC is perpendicular to AB. The problem asks to determine the potential at the mid-point of the line BC, point P (not shown).
My approach was to determine the distance AP. Then use $V_1=k\frac{Q_1}{AP}$ (where $V_1$ is the potential at P due to $Q_1$) and then the fact that the potential due to $Q_2$ at P is the same as that on its surface, that is $V_2=k\frac{Q_2}{r_2}$.
However, the solution argues that since there is no net field inside the second sphere, the potential at P is the same as the potential at point B, the center of the sphere. And then proceeds to use $V_1=k\frac{Q_1}{AB}$.
My confusion is that since the net field inside the second sphere is 0, what is the reasoning behind $V_1=\frac{Q_1}{AB}$? By this argument, shouldn't the potential at P, due to $Q_1$ be equal to that on the surface of the second sphere (due to $Q_1$)?