If a conductor has a potential `V != 0` and there are no charges anywhere else outside, then

Options

A. there must be charges on the surface or inside itself.
B. there cannot be any charge in the body of the conductor.
C. there must be charges only on the surface.
D. both (a) and (b) are correct.

Explanation

To solve the question, we need to analyze the implications of a conductor having a non-zero potential \( V \) in the absence of external charges. Here's the step-by-step solution:

### Step 1: Understand the implications of a non-zero potential
When a conductor has a non-zero potential \( V \), it indicates that there is an electric field present. The potential being constant throughout the conductor means that the electric field inside the conductor is zero.

**Hint:** Remember that the electric field inside a conductor in electrostatic equilibrium is always zero.

### Step 2: Analyze the absence of external charges
The problem states that there are no charges outside the conductor. This implies that any potential present must be due to charges located within the conductor itself or on its surface.

**Hint:** Consider the sources of electric fields and potentials in electrostatics.

### Step 3: Determine the presence of charges
Since the conductor has a non-zero potential, it must have some charge distribution. This charge can either be on the surface of the conductor or within it. However, we know from electrostatic principles that charges in a conductor will redistribute themselves to the surface.

**Hint:** Recall that charges in a conductor will always move to the surface in electrostatic equilibrium.

### Step 4: Evaluate the statements
1. **There must be charge on the surface or inside itself:** This statement is true because the non-zero potential indicates the presence of charge.

2. **There cannot be any charge in the body of the conductor:** This statement is also true because if there were charges inside, it would create an electric field, contradicting the condition of zero electric field inside the conductor.

3. **There must be charge on the surface:** This statement is not necessarily true; while there may be charge on the surface, it is not compulsory for there to be charge present.

### Conclusion
Based on the analysis:
- Statement A (There must be charge on the surface or inside itself) is true.
- Statement B (There cannot be any charge in the body of the conductor) is true.
- Statement C (There must be charge on the surface) is not necessarily true.

Thus, the correct answer is that both A and B are correct.

**Final Answer:** A and B are correct.