Assertion: If electric potential remains constant along a path in electric field, then the electric field must be zero.
Reason: The negative of an electric potential gradient in a direction is equal to the component of electric field in that direction.

Options

A. If both assertion and reason are correct and reason is a correct explanation of the assertion.
B. If both assertion and reason are correct but reason is not the correct explanation of assertion.
C. If assertion is correct but reason is incorrect.
D. If assertion is incorrect but reason is correct.

Answer

To solve the given question, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that "If electric potential remains constant along a path in an electric field, then the electric field must be zero."
- If the electric potential (V) is constant along a path, it implies that there is no change in potential energy as we move along that path.

2. **Understanding the Reason**:
- The reason states that "The negative of an electric potential gradient in a direction is equal to the component of electric field in that direction."
- Mathematically, this can be expressed as:
\[ E = -\frac{dV}{dx} \]
- This means that the electric field (E) is related to how the electric potential (V) changes with position (x). If the potential is constant, then the gradient (or derivative) is zero, leading to zero electric field in that direction.

3. **Analyzing the Assertion**:
- The assertion is incorrect because even if the electric potential is constant along a path, it does not necessarily mean that the electric field is zero. The electric field can still exist but may be perpendicular to the path taken.
- For example, in the case of an equipotential surface, the electric field lines are perpendicular to the surface, meaning the potential is constant along the surface, but the electric field is not zero.

4. **Conclusion**:
- The assertion is **incorrect** because the electric field can be non-zero even when the potential is constant along a path.
- The reason is **correct** because it accurately describes the relationship between electric field and potential gradient.

5. **Final Answer**:
- The assertion is incorrect, and the reason is correct. Therefore, the correct choice is that the assertion is false, and the reason is true.