Statement 1: Electric field produced by changing magnetic field is nonconservative.
Statement 2: For the electric field `vec E` induced by a changing magnetic field which has closed lines of force, `oint vec E . vec(dl) =0`

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 but statement-2 is false
D. Statement-1 is false, Statement-2 is true

Answer

To analyze the statements provided in the question, we can break down the reasoning step by step.

### Step 1: Understand Statement 1
**Statement 1:** Electric field produced by changing magnetic field is non-conservative.

- A conservative electric field is one where the work done around any closed loop is zero. This means that the electric field can be derived from a scalar potential.
- However, when a magnetic field changes with time, it induces an electric field according to Faraday's law of electromagnetic induction. This induced electric field does not have a potential associated with it, which means that the work done around a closed loop is not zero.

**Conclusion for Statement 1:** This statement is true.

### Step 2: Understand Statement 2
**Statement 2:** For the electric field \( \vec{E} \) induced by a changing magnetic field which has closed lines of force, \( \oint \vec{E} \cdot d\vec{l} = 0 \).

- The integral \( \oint \vec{E} \cdot d\vec{l} \) represents the work done by the electric field around a closed path.
- As established in Statement 1, the electric field induced by a changing magnetic field is non-conservative, which means that the work done around a closed loop is not zero. Therefore, \( \oint \vec{E} \cdot d\vec{l} \neq 0 \).

**Conclusion for Statement 2:** This statement is false.

### Final Conclusion
- **Statement 1 is true:** The electric field produced by a changing magnetic field is non-conservative.
- **Statement 2 is false:** The integral \( \oint \vec{E} \cdot d\vec{l} = 0 \) is incorrect for the electric field induced by a changing magnetic field.

### Summary
- **True Statement:** Statement 1
- **False Statement:** Statement 2

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