The armature coil of dynamo is in motion . The generated induced emf varies and the number of magnetic lines of force also varies . Which of the following condition is correct :-

Options

A. lines of flux will be minimum, but induced emf will be zero
B. lines of flux will be maximum, but the induced emf will be zero
C. line of flux will be maximum, but induced emf will be not be zero .
D. the lines of flux will be maximum, and the induced emf will be also maximum.

Answer

To solve the problem regarding the conditions of induced EMF and magnetic flux in the armature coil of a dynamo, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- The armature coil of a dynamo is rotating in a magnetic field. The magnetic field lines and the area vector of the coil determine the magnetic flux through the coil.

2. **Magnetic Flux Calculation**:
- The magnetic flux (Φ) through the 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.

3. **Rotation of the Coil**:
- As the coil rotates, the angle \(\theta\) changes. If the coil is rotated with a uniform angular velocity \(\omega\), then \(\theta\) can be expressed as:
\[ \theta = \omega t \]
- Thus, the magnetic flux can be rewritten as:
\[ \Phi(t) = B \cdot A \cdot \cos(\omega t) \]

4. **Induced EMF Calculation**:
- The induced EMF (E) in the coil can be calculated using Faraday's law of electromagnetic induction:
\[ E = -n \frac{d\Phi}{dt} \]
where \(n\) is the number of turns in the coil.

5. **Differentiating the Flux**:
- To find the induced EMF, we differentiate the magnetic flux:
\[ \frac{d\Phi}{dt} = -B \cdot A \cdot \omega \sin(\omega t) \]
- Therefore, the induced EMF becomes:
\[ E = n B A \omega \sin(\omega t) \]

6. **Analyzing Conditions**:
- The induced EMF is a function of \(\sin(\omega t)\), which means it will be zero when \(\omega t\) is an integer multiple of \(\pi\) (0, π, 2π, ...).
- The magnetic flux, however, is at its maximum when \(\cos(\omega t)\) is at its maximum (1 or -1), which occurs at the same points.

7. **Conclusion**:
- Therefore, when the magnetic flux is maximum, the induced EMF is zero. This leads us to conclude that the correct condition is:
- "Lines of flux will be maximum but induced EMF will be zero."

### Final Answer:
The correct condition is: **Lines of flux will be maximum but induced EMF will be zero.**

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