Assertion : Motional induced emf `e = Bvl` can be derived from the relation `e = -(d\phi)/(dt)`
Reason : Lenz's law is a consequence of law of conservation of energy.

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.

Answer

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Understanding the Assertion
The assertion states that the motional induced EMF \( e = Bvl \) can be derived from the relation \( e = -\frac{d\phi}{dt} \).

1. **Identify the terms**:
- \( e \) is the induced EMF.
- \( B \) is the magnetic field strength.
- \( v \) is the velocity of the conductor.
- \( l \) is the length of the conductor in the magnetic field.

2. **Relate the two equations**:
- The magnetic flux \( \phi \) through a loop is given by \( \phi = B \cdot A \), where \( A \) is the area.
- If the loop is moving with velocity \( v \), the area \( A \) changes over time, which can be expressed as \( A = l \cdot x \) where \( x \) is the distance moved.

3. **Differentiate the flux**:
- The rate of change of magnetic flux is given by:
\[ \frac{d\phi}{dt} = B \frac{dA}{dt} \]
- If the area \( A \) is changing due to the motion of the loop, we can express \( \frac{dA}{dt} \) in terms of the velocity \( v \):
\[ \frac{dA}{dt} = l \cdot v \]
- Therefore, substituting this back, we get:
\[ \frac{d\phi}{dt} = B \cdot (l \cdot v) \]
- The induced EMF can then be expressed as:
\[ e = -\frac{d\phi}{dt} = -Bvl \]

### Step 2: Understanding the Reason
The reason states that Lenz's law is a consequence of the law of conservation of energy.

1. **Define Lenz's Law**:
- Lenz's law states that the direction of the induced current is such that it opposes the change in magnetic flux that produced it.

2. **Connection to Conservation of Energy**:
- This opposition ensures that energy is conserved in the system. If the induced current did not oppose the change, it would lead to a situation where energy could be created from nothing, violating the conservation of energy principle.

### Conclusion
Both the assertion and reason are true, and the reason correctly explains the assertion.

### Final Answer
Both the assertion and the reason are true, and the reason is the correct explanation of the assertion.