A wire loop is rotated in magneitc field. The frequency of change of direction of the induced e.m.f. is.

Options

A. Six times per revolution
B. Once per rovolution
C. twice per revolution
D. four times per revolution

Explanation

To determine the frequency of change of direction of the induced e.m.f. in a wire loop that is rotating in a magnetic field, we can follow these steps:

### Step 1: Understand the Induced EMF
When a wire loop rotates in a magnetic field, an electromotive force (e.m.f.) is induced in the loop. The induced e.m.f. can be expressed mathematically as:
\[ E = E_0 \sin(\omega t) \]
where \( E_0 \) is the maximum e.m.f., \( \omega \) is the angular frequency, and \( t \) is time.

### Step 2: Analyze the Sine Function
The sine function oscillates between -1 and 1. This means that the induced e.m.f. will also oscillate between \( -E_0 \) and \( E_0 \).

### Step 3: Determine the Direction Changes
The sine function changes its direction:
- From positive to negative (crossing zero)
- From negative to positive (crossing zero again)

In one complete cycle of the sine wave (from 0 to \( 2\pi \)), the function crosses the zero line twice:
1. Once when it goes from positive to negative.
2. Once when it goes from negative to positive.

### Step 4: Calculate the Frequency of Direction Change
Since the sine function completes one full cycle (one revolution of the loop) in a time period \( T \), and it changes direction twice in that time period, the frequency of change of direction \( f \) is given by:
\[ f = \frac{2}{T} \]
where \( T \) is the time period of one complete cycle.

### Step 5: Conclusion
Thus, the frequency of change of direction of the induced e.m.f. is twice the frequency of rotation of the loop. Therefore, if the loop completes one full rotation (one cycle) in time \( T \), the frequency of change of direction is:
\[ f = 2 \times \text{(frequency of rotation)} \]

### Final Answer
The frequency of change of direction of the induced e.m.f. is **2 times per revolution**.

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