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In the following question a statement of...

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.

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).

Text Solution

AI Generated Solution

The correct Answer is:
To solve the assertion and reason question, we need to analyze both statements carefully. ### Step 1: Understand the Assertion The assertion states: "For a given potential function, electric intensity function can be uniquely derived." - **Explanation**: The electric field intensity (E) is related to the electric potential (V) through the relationship: \[ E = -\frac{dV}{dr} \] This implies that if we know the potential function V(r), we can differentiate it to find the electric field intensity E. Therefore, the assertion is true. ### Step 2: Understand the Reason The reason states: "For a given electric intensity function, electric potential function can be uniquely derived." - **Explanation**: The relationship between electric field intensity and electric potential is given by: \[ dV = -E \, dr \] To find the potential function V from the electric field intensity E, we would integrate: \[ V = -\int E \, dr \] However, this integration can yield a family of potential functions differing by a constant (since the potential is defined up to an arbitrary constant). Thus, the reason statement is false because the potential function is not uniquely determined by the electric field intensity. ### Step 3: Conclusion Based on the analysis: - The assertion is true. - The reason is false. Thus, the correct answer is that the assertion is true, but the reason is false. ### Final Answer The assertion is true, while the reason is false. ---
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