STATEMENT-1 `:` At a point electrostatic field is zero, then potential at that point may be zero .
and
STATEMENT-2 `:` Negative of the potential gradient is equal to electrostatic field.

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1
B. Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1
C. Statement-1 is True, Statement-2 is False
D. Statement-1 is False , Statement-2 is True

Answer

To analyze the given statements, we will break down the reasoning step by step.

### Step 1: Understand Statement 1
**Statement 1:** At a point where the electric field is zero, the potential at that point may be zero.

- The electric field (E) is related to the electric potential (V) by the equation:
\[ E = -\frac{dV}{dr} \]
- If the electric field (E) is zero at a point, it implies:
\[ -\frac{dV}{dr} = 0 \]
- This means that the derivative of the potential with respect to distance is zero, indicating that the potential (V) could be constant.

### Step 2: Analyze the Implications of the Derivative Being Zero
- If the derivative of V is zero, it means that V does not change with respect to r. Therefore, V could be:
- A constant value (which could be any number, including zero).
- Specifically, V could be zero, but it could also be some other constant value (like 5 volts, 10 volts, etc.).

### Conclusion for Statement 1
- Thus, Statement 1 is **true** because the potential at that point can indeed be zero, but it is not necessarily zero; it could be any constant value.

### Step 3: Understand Statement 2
**Statement 2:** The negative of the potential gradient is equal to the electrostatic field.

- The potential gradient is defined as:
\[ \text{Potential Gradient} = \frac{dV}{dr} \]
- According to the relationship between electric field and potential:
\[ E = -\frac{dV}{dr} \]
- This confirms that the negative of the potential gradient is indeed equal to the electric field.

### Conclusion for Statement 2
- Therefore, Statement 2 is also **true**.

### Final Conclusion
- Both statements are true, and Statement 2 serves as an explanation for Statement 1. Thus, the correct answer is that both statements are true.

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