Statement -1 : The work done by induced electric field along a closed path is zero.
Statement -2 : The induced electric field is non - conservative.

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, Statement-2 is False.
D. Statement -1 is False , Statement-2 ,is ture.

Answer

To analyze the given statements, we will break down the problem step by step.

### Step 1: Understanding Statement 1
**Statement 1:** "The work done by induced electric field along a closed path is zero."

To evaluate this statement, we need to understand the nature of the induced electric field. In electromagnetic induction, the induced electric field is generated due to a changing magnetic field. One key property of the induced electric field is that it is non-conservative.

### Step 2: Understanding Statement 2
**Statement 2:** "The induced electric field is non-conservative."

A non-conservative electric field means that the work done by the field depends on the path taken and not just on the initial and final points. For a conservative field, the work done around any closed path would be zero.

### Step 3: Analyzing the Work Done
To determine the work done by the induced electric field along a closed path, we can use the concept of electromotive force (EMF). The work done by an electric field \( E \) along a path \( L \) can be expressed as:

\[ W = \oint E \cdot dL \]

For a non-conservative field, this integral is not necessarily zero. In fact, it is related to the rate of change of magnetic flux (\( \Phi \)) through the area enclosed by the path:

\[ \oint E \cdot dL = -\frac{d\Phi}{dt} \]

Since \( \frac{d\Phi}{dt} \) can be non-zero when there is a changing magnetic field, the work done around a closed path is also non-zero.

### Step 4: Conclusion
From our analysis:
- **Statement 1** is **false** because the work done by the induced electric field along a closed path is not zero.
- **Statement 2** is **true** because the induced electric field is indeed non-conservative.

Thus, the correct conclusion is:
- Statement 1 is false.
- Statement 2 is true.

### Final Answer
- Statement 1: False
- Statement 2: True