A wire loop is rotated in magneitc field. The frequency of change of direction of the induced e.m.f. is.
(1.) Once per revolution
(2.) twice per revolution
(3.) four times per revoution
(4.) six time per revolution

Options

A. Once per revolution
B. twice per revolution
C. four times per revoution
D. six time per revolution

Explanation

To solve the problem of determining the frequency of change of direction of the induced e.m.f. when a wire loop is rotated in a magnetic field, we can follow these steps:

### Step 1: Understand the Basics of Electromagnetic Induction
When a wire loop is rotated in a magnetic field, it experiences a change in magnetic flux. According to Faraday's law of electromagnetic induction, this change in flux induces an electromotive force (e.m.f.) in the loop.

**Hint 1:** Recall that the induced e.m.f. is related to the rate of change of magnetic flux through the loop.

### Step 2: Analyze the Rotation of the Loop
As the loop rotates, the angle between the magnetic field and the normal to the loop changes. The magnetic flux through the loop can be expressed as:
\[ \Phi = B \cdot A \cdot \cos(\theta) \]
where \( \Phi \) is the magnetic flux, \( B \) 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.

**Hint 2:** Remember that the angle \( \theta \) changes as the loop rotates, affecting the magnetic flux.

### Step 3: Determine the Change in Flux
When the loop is perpendicular to the magnetic field, the flux is at its maximum. As it rotates to a position parallel to the magnetic field, the flux decreases to zero. Continuing to rotate, the flux becomes negative when the loop is again perpendicular but in the opposite direction.

**Hint 3:** Visualize the loop's rotation and how the flux changes from maximum to zero to maximum in the opposite direction.

### Step 4: Identify the Direction Change of Induced e.m.f.
The induced e.m.f. changes direction whenever the magnetic flux changes from increasing to decreasing or vice versa. This occurs twice during one complete revolution of the loop:
1. From maximum positive flux to zero (first change).
2. From zero to maximum negative flux (second change).

**Hint 4:** Consider how many times the induced e.m.f. changes direction as the loop completes one full rotation.

### Step 5: Conclusion
Based on the analysis, the frequency of change of direction of the induced e.m.f. is twice per revolution.

**Final Answer:** The frequency of change of direction of the induced e.m.f. is **(2) twice per revolution**.