Final answer:
When two identical metal spheres connected by a plastic rod are initially neutral, adding electrons to one of the spheres will redistribute charge between them. After removing the rod, both spheres will have an equal magnitude of charge but opposite signs. Therefore, sphere B will have a negative charge equal to the excess electrons added to sphere A.
Step-by-step explanation:
When two identical metal spheres are connected by a plastic rod and initially neutral, adding electrons to one of the spheres will cause a redistribution of charge between the spheres. Since the spheres are conductors, the excess electrons on sphere A will spread out on both spheres due to repulsion. After removing the connecting rod, both spheres will have an equal magnitude of charge but opposite signs. Therefore, sphere B will have a negative charge equal in magnitude to the excess electrons added to sphere A.
Let's say the total charge on sphere A is Q. In this case, Q = 3.0 × 1012 electrons. Since sphere B and A have equal magnitudes of charge after separation, the charge on sphere B will also be Q, but with a negative sign. Therefore, the charge on sphere B will be -3.0 × 1012 electrons.
To summarize, the charge of sphere B after the connecting rod is removed will be -3.0 × 1012 electrons.