When the wire loop is rotated in the magnetic field between the poles of a magnet the frequency of emf is

Options

A. 1 revolution
B. 2 revolution
C. 1/4 revolution
D. 1/2 revolution

Explanation

To solve the problem of determining the frequency of EMF generated when a wire loop is rotated in a magnetic field, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a wire loop rotating in a magnetic field created by a magnet. The magnetic field lines are directed from one pole of the magnet to the other.

2. **Magnetic Flux Calculation**:
- The magnetic flux (Φ) through the loop 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 loop,
- \(\theta\) is the angle between the magnetic field and the normal to the surface of the loop.

3. **Induced EMF Calculation**:
- According to Faraday's law of electromagnetic induction, the induced EMF (ε) in the loop is given by the rate of change of magnetic flux:
\[ \epsilon = -\frac{d\Phi}{dt} = -\frac{d(B \cdot A \cdot \cos(\theta))}{dt} \]
- As the loop rotates, \(\theta\) changes, which affects the cosine term.

4. **Analyzing the Rotation**:
- When the loop completes one full rotation (360 degrees or \(2\pi\) radians), the angle \(\theta\) changes from 0 to \(2\pi\).
- The cosine function oscillates between +1 and -1, meaning the EMF will be positive for half the rotation (0 to \(\pi\)) and negative for the other half (\(\pi\) to \(2\pi\)).

5. **Frequency of EMF**:
- Since the EMF changes its sign twice during one complete revolution (once at \(\pi\) and once at \(2\pi\)), the frequency of the EMF can be defined as:
\[ \text{Frequency} = \frac{\text{Number of sign changes}}{\text{Time for one revolution}} \]
- In one full revolution, the EMF changes sign twice, indicating that the frequency of the EMF is \(1\) cycle per revolution.

6. **Conclusion**:
- Therefore, the frequency of the induced EMF when the wire loop is rotated in the magnetic field is:
\[ \text{Frequency} = \frac{2}{T} \quad \text{(where T is the time for one complete revolution)} \]
- If we consider one complete revolution as one cycle, the frequency of the EMF is \(f = \frac{1}{T}\).