(A): The electric field induced due to changing magnetic field is non-conservative.
(R): The line integral of the electric field along a closed loop is always zero.

Options

A. Both A and R are true and R is the correct explanation
B. Both A and R are true but R is not the correct explanation of A
C. A is true but R is false
D. Both A and R are false

Answer

To solve the question, we need to analyze the statements given:

**Statement (A):** The electric field induced due to changing magnetic field is non-conservative.
**Statement (R):** The line integral of the electric field along a closed loop is always zero.

### Step 1: Understanding the Nature of Induced Electric Fields
The electric field induced by a changing magnetic field is indeed non-conservative. This is a fundamental concept in electromagnetism, specifically described by Faraday's law of electromagnetic induction. A non-conservative electric field means that the work done in moving a charge around a closed path in this field is not zero.

**Hint:** Recall Faraday's law of electromagnetic induction, which states that a changing magnetic field induces an electric field.

### Step 2: Evaluating the Line Integral of the Induced Electric Field
For a non-conservative electric field, the line integral of the electric field around a closed loop is not zero. According to Faraday's law, the induced electromotive force (emf) in a closed loop is equal to the negative rate of change of magnetic flux through the loop. This implies that the line integral of the electric field around a closed path is equal to the induced emf, which is generally not zero if there is a changing magnetic field.

**Hint:** Consider the implications of Faraday's law and how it relates to the work done in a closed loop.

### Step 3: Conclusion
From our analysis:
- Statement (A) is true: The electric field induced due to a changing magnetic field is non-conservative.
- Statement (R) is false: The line integral of the electric field along a closed loop is not always zero; it is non-zero in the presence of a changing magnetic field.

Thus, the correct answer is that (A) is true and (R) is false.

**Final Answer:** (A) is true, (R) is false.