Which of the following is correct for sinusoidal electromagnetic induction :

Options

A. maximum flux, zero emf
B. zero flux , maximum emf
C. zero flux , zero emf
D. (1) & (2) both

Answer

To solve the question regarding sinusoidal electromagnetic induction, we will analyze the concepts of magnetic flux, induced EMF, and their relationships in a sinusoidal context.

### Step-by-Step Solution:

1. **Understanding Magnetic Flux**:
- The magnetic flux (Φ) through a coil is given by the formula:
\[ \Phi = B \cdot A \cdot \cos(\theta) \]
where \(B\) is the magnetic field strength, \(A\) is the area of the coil, and \(\theta\) is the angle between the magnetic field and the normal to the surface of the coil.

2. **Setting Up the Scenario**:
- In sinusoidal electromagnetic induction, we consider a coil with \(N\) turns placed in a uniform magnetic field \(B\). The area vector \(A\) is perpendicular to the plane of the coil. As the coil rotates with an angular velocity \(\omega\), the angle \(\theta\) changes with time.

3. **Expressing Flux as a Function of Time**:
- As the coil rotates, the angle \(\theta\) can be expressed as:
\[ \theta = \omega t \]
- Thus, the magnetic flux as a function of time becomes:
\[ \Phi(t) = NAB \cos(\omega t) \]

4. **Induced EMF Calculation**:
- According to Faraday's law of electromagnetic induction, the induced EMF (ε) is given by:
\[ \epsilon = -\frac{d\Phi}{dt} \]
- Differentiating the flux with respect to time:
\[ \epsilon = -\frac{d}{dt}(NAB \cos(\omega t)) = NAB \omega \sin(\omega t) \]

5. **Analyzing Maximum and Zero Values**:
- The maximum flux occurs when \(\sin(\omega t) = 1\), which happens at \(\omega t = \frac{\pi}{2} + n\pi\) (where \(n\) is an integer).
- The induced EMF is zero when the flux is at its maximum, as \(\sin(\omega t)\) is zero at these points.

6. **Conclusion**:
- From the analysis, we conclude:
- Maximum flux corresponds to zero EMF.
- Zero flux corresponds to maximum EMF.
- Therefore, the correct statements regarding sinusoidal electromagnetic induction are:
- Maximum flux leads to zero EMF.
- Zero flux leads to maximum EMF.

### Final Answer:
The correct options are:
1. Maximum flux corresponds to zero EMF.
2. Zero flux corresponds to maximum EMF.