A

Step 1: When an uncharged conductor A is brought close to a positively charged conductor B, electrostatic induction occurs.
Step 2: The positive charges in conductor B induce a negative charge on the side of conductor A that is closer to B, while the far side of A acquires a positive charge.
Step 3: As the distance between the conductors decreases, the electric field around B influences A, resulting in the redistribution of charges.
Step 4: The total charge of conductor A remains zero because it was uncharged initially. However, the induced negative charges on A do not affect the overall charge of conductor B.
Step 5: Therefore, the net charge on B remains constant, although the electric field strength (and thus the potential) in its vicinity may increase.
Therefore, the charge on B will remain constant while the potential increases due to the presence of A and its interaction with the electric field created by B.
The correct answer is option A: will increase but potential will be constant.