Mark the correct statements.

Options

A. A given conducting sphere cannot be charged to a potential greater than a certain value.
B. A given conducting sphere can be charged to a potential less than a certain minimum value.
C. A given conducting sphere can be charged to any extent.
D. none of these

Explanation

To solve the question, we need to analyze the statements about a conducting sphere and determine which ones are correct. Let's go through each statement step by step.

### Step 1: Analyze Statement A
**Statement A:** "A given conducting sphere cannot be charged to a potential greater than a certain value."

- A conducting sphere has a limit to how much charge it can hold, which is influenced by the dielectric strength of the surrounding medium. If the charge exceeds this limit, it can lead to breakdown of the medium, causing a discharge.
- Therefore, this statement is **correct**.

### Step 2: Analyze Statement B
**Statement B:** "A given conducting sphere can be charged to a potential less than a certain minimum value."

- A conducting sphere can indeed be charged to any potential from zero up to its maximum potential, which is determined by the dielectric strength of the medium. There is no lower limit to the charge; it can be uncharged (0 potential) or charged to any value less than the maximum.
- Thus, this statement is also **correct**.

### Step 3: Analyze Statement C
**Statement C:** "A conducting sphere can be charged to any extent."

- This statement implies that there is no limit to the amount of charge that can be placed on the sphere. However, as previously discussed, there is a maximum limit due to the dielectric strength of the medium. Charging beyond this limit would not be possible.
- Therefore, this statement is **incorrect**.

### Conclusion
The correct statements are:
- **A**: A given conducting sphere cannot be charged to a potential greater than a certain value. (Correct)
- **B**: A given conducting sphere can be charged to a potential less than a certain minimum value. (Correct)
- **C**: A conducting sphere can be charged to any extent. (Incorrect)

### Final Answer
The correct options are **A and B**.

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