when the wire loop is rotated in the magnetic field between the poles of a magnet the direction of emf changes once in every

Options

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

Explanation

To solve the question regarding the change in direction of emf when a wire loop is rotated in a magnetic field, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Magnetic Flux**:
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, and \(\theta\) is the angle between the magnetic field and the normal to the surface of the loop.

**Hint**: Remember that the angle \(\theta\) changes as the loop rotates.

2. **Induced EMF**:
According to Faraday's law of electromagnetic induction, the induced emf (ε) in the loop is given by:
\[ \epsilon = -\frac{d\Phi}{dt} \]
This means that the emf is related to the rate of change of magnetic flux through the loop.

**Hint**: The negative sign indicates the direction of induced emf as per Lenz's law.

3. **Rotation of the Loop**:
As the loop rotates, the angle \(\theta\) changes continuously. For one complete revolution (360 degrees or \(2\pi\) radians), the angle \(\theta\) varies from \(0\) to \(2\pi\).

**Hint**: Consider how the angle \(\theta\) affects the cosine function in the flux equation.

4. **Change in Sign of EMF**:
As the loop rotates from \(0\) to \(180\) degrees (\(0\) to \(\pi\)), the value of \(\cos(\theta)\) changes from positive to negative. This means that the emf will change its sign once during this half revolution.

**Hint**: Focus on the intervals of rotation to see when the emf changes direction.

5. **Complete Revolution Analysis**:
In a complete revolution (from \(0\) to \(2\pi\)), the emf changes sign twice:
- From \(0\) to \(\pi\): emf is positive.
- From \(\pi\) to \(2\pi\): emf is negative.

**Hint**: Count the number of times the emf changes sign in one full rotation.

6. **Conclusion**:
Therefore, the direction of emf changes once in every half revolution. Since there are two half revolutions in one complete revolution, the answer to the question is:
- The direction of emf changes once in every half revolution.

**Final Answer**: The direction of emf changes once in every half revolution.