In the following question a statement of assertion (A) is followed by a statement of reason (R )
A: For a given potential function, electric intensity function can be uniquely derived.
R : For a given electric intensity function, electric potential function can be uniquely derived.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion , then mark (1).
B. If both Assertion & Reason are true but the reason is not correct explanation of the assertion then mark (2)
C. If Assertion is true statement but Reason is false, then mark (3)
D. If both Assertion and Reason are false statements , then mark (4).

Answer

To analyze the given assertion (A) and reason (R), we will break down the statements and derive the necessary conclusions step by step.

### Step 1: Understanding the Assertion (A)
The assertion states: "For a given potential function, the electric intensity function can be uniquely derived."

- The electric potential \( V \) is related to the electric field \( \mathbf{E} \) by the equation:
\[ \mathbf{E} = -\nabla V \]
- This means that if we have a specific potential function \( V \), we can differentiate it to find the electric field \( \mathbf{E} \). Therefore, the assertion is **true**.

### Step 2: Understanding the Reason (R)
The reason states: "For a given electric intensity function, the electric potential function can be uniquely derived."

- The electric field \( \mathbf{E} \) is related to the electric potential \( V \) through the equation:
\[ V = -\int \mathbf{E} \cdot d\mathbf{r} \]
- When we integrate the electric field to find the potential, we introduce an arbitrary constant of integration. This means that the potential is not uniquely defined since different constants can yield different potential functions. Therefore, the reason is **false**.

### Step 3: Conclusion
Since the assertion is true and the reason is false, we conclude that the correct answer is that the assertion is true while the reason is false.

### Final Answer
- Assertion (A) is true.
- Reason (R) is false.