They are originally neutral. A positively charged rod is brought near (but not touching) the far end of A. While the charged rod is still close, A and B are separated. The charged rod is then withdrawn. Is the sphere then positively charged, negatively charged, or neutral?

The sphere returns back to the neutral.

Explanation:

When a positively charged rod is brought near the far end of the rod A a redistribution of the charges occurs in the rod A. The free electrons in the rod A are attracted towards the positively charged rod. This causes positive charges to be shifted towards the other end of the rod A. The sphere B is in contact with the positively charged end of rod A. So it also acquires a positive charge.

When the positively charged rod is removed from the faf end of rod A, the electrons return to their original state and the charges redistributes themselves and a neutral state is re-established .

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