Which of the following statements (s) `is//are` correct ?

Options

A. If the electric field due to a point charge varies as `r^(-2.5)` instead of `r^(-2)`, then Gauss's law will still be valid.
B. Gauss's law can be used to calculate the field distribution around an electric dipole.
C. If the electric field between two point charges is zero somewhere, then the sign of the two charges is the same.
D. The work done by the external force is moving a unit positive charge from point A at potential `V_A` to point B at potential `V_B is (V_B - V_A)` .

Explanation

To determine which of the statements are correct, we will analyze each statement one by one based on the principles of electrostatics and Gauss's law.

### Step-by-Step Solution:

1. **Statement 1**: "If the electric field due to a point charge varies as r raised to the power of -2.5 instead of r square, then Gauss's law will still be valid."
- **Analysis**: Gauss's law is valid when the electric field \(E\) due to a point charge varies as \(E \propto \frac{1}{r^2}\). If the electric field varies as \(E \propto \frac{1}{r^{2.5}}\), it does not follow the inverse square law. Therefore, Gauss's law is not applicable in this case.
- **Conclusion**: This statement is **incorrect**.

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