An uncharged conductor A is brought near a positively charged conductor B. The size of the conductor A is much greater than the size of conductor B. Then,

Options

A. the charge on `B` will increase, but the potential of `B` will not change.
B. the charge on `B` will not change, but the potential of `B` will decrease.
C. the charge on `B` will decrease, but the potential of `B` will not change.
D. the charge on `B` will not change, but the potential of `B` will increase.

Explanation

To solve the problem step by step, we will analyze the situation of the uncharged conductor A being brought near the positively charged conductor B.

### Step 1: Understand the Situation
- We have two conductors: conductor A (uncharged) and conductor B (positively charged).
- The size of conductor A is much larger than that of conductor B.

### Step 2: Induction of Charges
- When the uncharged conductor A is brought near the positively charged conductor B, the electric field from the positive charge on B will influence the charges in A.
- The positive charge on B will attract the negative charges in A towards itself, causing the surface of A closest to B to become negatively charged.
- Consequently, the side of A that is farthest from B will become positively charged due to the repulsion of the positive charges in A.

### Step 3: Charge Distribution on Conductor A
- The charge distribution on conductor A will be such that:
- The side of A nearest to B will have a negative charge (induced).
- The side of A farthest from B will have a positive charge.
- However, the total net charge on conductor A remains zero since it was initially uncharged.

### Step 4: Effect on Potential
- The presence of the positive charge on conductor B will influence the electric potential around it.
- The potential \( V \) at a point due to a charge is given by the formula \( V = k \frac{Q}{R} \), where \( k \) is Coulomb's constant, \( Q \) is the charge, and \( R \) is the distance from the charge.
- Since the negative charge induced on A is closer to B, it will affect the potential experienced by A.

### Step 5: Conclusion on Charge and Potential
- The charge on conductor B remains unchanged because the system is isolated and the introduction of A does not add or remove charge from B.
- The potential of conductor B will decrease due to the presence of the induced negative charge on A, which effectively reduces the electric field strength at the location of B.

### Final Summary
- The net charge on conductor A remains zero.
- The charge on conductor B remains unchanged.
- The potential of conductor B decreases due to the induced charges on conductor A.