Assertion : Electric field produced by a variable magnetic field can't exert a force on a charged particle.
Reason : This electric field is non-conservative in nature.

Options

A. If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion
C. If Assertion is true, but the Reason is false.
D. If Assertion is false but the Reason is true.

Explanation

To analyze the given assertion and reason, let's break down the concepts step by step.

### Step 1: Understanding the Assertion
The assertion states that "the electric field produced by a variable magnetic field can't exert a force on a charged particle."

- **Explanation**: According to electromagnetic theory, a changing magnetic field induces an electric field (as per Faraday's Law of Electromagnetic Induction). This induced electric field can exert a force on a charged particle. Therefore, the assertion is incorrect.

### Step 2: Understanding the Reason
The reason states that "this electric field is non-conservative in nature."

- **Explanation**: A non-conservative electric field means that the work done by the electric field around a closed loop is not zero. In the case of a variable magnetic field, the induced electric field does indeed do work on charges moving in a closed path, indicating that it is non-conservative. This part of the statement is true.

### Step 3: Evaluating the Assertion and Reason Together
Now we need to evaluate the truth of both the assertion and the reason:

- The assertion is **false** because the electric field produced by a variable magnetic field **can** exert a force on a charged particle.
- The reason is **true** because the electric field produced by a variable magnetic field is indeed non-conservative.

### Conclusion
Based on the evaluation:
- The assertion is false.
- The reason is true.

Thus, the correct option is that the assertion is false, and the reason is true.

### Final Answer
The assertion is false, and the reason is true. Therefore, the correct option is D.

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