A magnet is moved towards the coil

Options

A. (i) quickly
B. (ii)slowly
then the induced emf is
C. A.Larger in case (i)
D. B.Smaller in case (i)

Answer

**Step-by-Step Solution:**

1. **Understanding the Setup**: We have a coil and a magnet. The magnet has a north and south pole, and it is moving towards the coil. The movement can be either fast or slow.

2. **Identifying the Key Concepts**: According to Faraday's Law of Electromagnetic Induction, the induced electromotive force (EMF) in a coil is proportional to the rate of change of magnetic flux through the coil. The magnetic flux (Φ) is given by the product of the magnetic field (B) and the area (A) of the coil:
\[ \Phi = B \cdot A \]

3. **Analyzing the Movement of the Magnet**:
- **Case 1 (Fast Movement)**: When the magnet moves quickly towards the coil, the change in magnetic flux occurs rapidly. This means that the time interval (Δt) for this change is small.
- **Case 2 (Slow Movement)**: When the magnet moves slowly, the change in magnetic flux occurs over a longer time interval (Δt is larger).

4. **Applying Faraday's Law**: The induced EMF (ε) can be expressed as:
\[ \epsilon = -\frac{d\Phi}{dt} \]
Since the magnetic field (B) and the area (A) of the coil are constant, the induced EMF depends on the rate of change of magnetic flux, which is inversely related to the time interval (Δt).

5. **Comparing the Two Cases**:
- In **Case 1 (Fast Movement)**: The small Δt leads to a larger induced EMF.
- In **Case 2 (Slow Movement)**: The larger Δt leads to a smaller induced EMF.

6. **Conclusion**: Since the question asks for the case in which the induced EMF is greater, we conclude that the induced EMF is larger when the magnet is moving quickly towards the coil (Case 1).

**Final Answer**: The induced EMF is larger in Case 1 (when the magnet is moving quickly towards the coil).

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