Final answer:
The resulting charge distribution on the conducting sphere when a positively charged rod is brought near it is characterized by induced polarization, creating negative charge on the near side and positive charge on the far side.
Step-by-step explanation:
When a positively charged insulating rod is brought near a neutral conducting sphere, the electrons within the sphere are attracted to the side closest to the charged rod. This separation of charge within the sphere is called induced polarization. The side of the sphere nearest to the rod acquires a negative charge due to the attracted electrons, while the far side of the sphere becomes positively charged owing to a deficit of electrons. Although the conducting sphere remains overall electrically neutral, this charge separation creates a scenario where the sphere can now exert an electric force on nearby charges, and it will be attracted to the positively charged rod.
This phenomenon does not require any contact between the sphere and the rod. The result is the distribution of charge on the surface of the conducting sphere that is non-uniform, with negative charge accumulating on the side nearest the charged rod and positive charge on the opposite side.