A wire loop is rotated in a uniform magnetic field about an an axis perpendicular to the field. The direction of the current induced in the loop reverses once each

Options

A. quarter revolution
B. half revolution
C. full revolution
D. two revolutions

Explanation

To determine how often the direction of the induced current in a wire loop reverses when the loop is rotated in a uniform magnetic field, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a wire loop that is rotating in a uniform magnetic field. The axis of rotation is perpendicular to the magnetic field lines.

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, and \(\theta\) is the angle between the magnetic field and the normal to the loop's surface.

3. **Rotation of the Loop**:
- As the loop rotates, the angle \(\theta\) changes with time. If the loop rotates with an angular velocity \(\omega\), then:
\[ \theta = \omega t \]

4. **Flux Variation Over Time**:
- At \(t = 0\), \(\theta = 0\) and the flux is maximum (\(\Phi_{max} = B \cdot A\)).
- As time progresses, the angle increases, and the flux decreases until \(\theta = 90^\circ\) (or \(\frac{\pi}{2}\) radians), at which point the flux is zero.

5. **Flux Reversal**:
- After reaching zero at \(90^\circ\), as the loop continues to rotate to \(180^\circ\), the flux becomes negative (indicating a reversal in direction). The flux reaches its minimum value at \(180^\circ\).

6. **Induced Current Direction**:
- According to Lenz's Law, the induced current will flow in such a way as to oppose the change in magnetic flux.
- From \(0^\circ\) to \(90^\circ\), the flux decreases, and the induced current flows in one direction (let's say clockwise).
- From \(90^\circ\) to \(180^\circ\), the flux increases in the negative direction, causing the induced current to reverse (now flowing anti-clockwise).

7. **Conclusion**:
- The current reverses its direction every half revolution (i.e., every \(180^\circ\)) of the loop's rotation.

### Final Answer:
The direction of the current induced in the loop reverses once every half revolution.