In EMI, line integral of induced field around a closed path is .............. and induced electric field is ................

Options

A. zero, non-conservative
B. non-zero, non-conservative
C. non-zero, conservative
D. zero, conservative

Explanation

To solve the question regarding the line integral of the induced electric field in Electromagnetic Induction (EMI) and its nature, we will break it down step by step.

### Step 1: Understanding the Concept of Induced Electric Field
In the context of electromagnetic induction, an electric field can be induced in a closed loop due to a changing magnetic field. This induced electric field is a result of Faraday's law of electromagnetic induction.

**Hint:** Recall Faraday's law which states that a changing magnetic field induces an electromotive force (EMF) in a closed loop.

### Step 2: Line Integral of Induced Electric Field
The line integral of the induced electric field \( \mathbf{E} \) around a closed path is given by:

\[ \oint \mathbf{E} \cdot d\mathbf{l} = -\frac{d\Phi_B}{dt} \]

where \( \Phi_B \) is the magnetic flux through the loop. If the magnetic flux is changing, the right-hand side of the equation is non-zero, which means:

\[ \oint \mathbf{E} \cdot d\mathbf{l} \neq 0 \]

**Hint:** Remember that the line integral is related to the change in magnetic flux through the loop.

### Step 3: Nature of the Induced Electric Field
The induced electric field in this scenario is non-conservative. This means that the work done in moving a charge around a closed path in the induced electric field is not zero, which is a characteristic of non-conservative fields.

**Hint:** Think about the difference between conservative and non-conservative fields. In conservative fields, the work done around a closed loop is zero.

### Step 4: Conclusion
Based on the above analysis, we can conclude that:

- The line integral of the induced electric field around a closed path is **non-zero**.
- The induced electric field is **non-conservative**.

Thus, the correct answer to the question is:
- Line integral of induced field around a closed path is **non-zero**.
- Induced electric field is **non-conservative**.

### Final Answer:
- Line integral of induced field around a closed path is **non-zero**.
- Induced electric field is **non-conservative**.