A wire of length 1 metre is to be wound in the form of a coil have maximum magnetic moment. The suitable number of turns among the following is

Options

A. 1
B. 1000
C. independent of no of turns
D. none

Answer

To solve the problem of determining the suitable number of turns for a coil made from a 1-meter wire to achieve maximum magnetic moment, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Magnetic Moment**:
The magnetic moment \( M \) of a coil is given by the formula:
\[ M = N \cdot I \cdot A \]
where \( N \) is the number of turns, \( I \) is the current flowing through the coil, and \( A \) is the area of the coil.

2. **Relating Wire Length to Number of Turns**:
The length of the wire \( L \) is related to the number of turns \( N \) and the radius \( R \) of the coil by the equation:
\[ L = N \cdot 2\pi R \]
Given that the length of the wire \( L = 1 \) meter, we can express \( N \) in terms of \( R \):
\[ N = \frac{L}{2\pi R} = \frac{1}{2\pi R} \]

3. **Area of the Coil**:
The area \( A \) of a circular coil is given by:
\[ A = \pi R^2 \]

4. **Substituting Area in Magnetic Moment**:
Substituting the expression for \( A \) into the magnetic moment formula gives:
\[ M = N \cdot I \cdot \pi R^2 \]
Replacing \( N \) with \( \frac{1}{2\pi R} \):
\[ M = \left(\frac{1}{2\pi R}\right) \cdot I \cdot \pi R^2 \]
Simplifying this:
\[ M = \frac{IR}{2} \]

5. **Maximizing Magnetic Moment**:
To maximize \( M \), we need to maximize \( R \). However, as \( R \) increases, \( N \) decreases since \( N = \frac{1}{2\pi R} \). The maximum magnetic moment occurs when \( N = 1 \) because this allows for the largest area for a given length of wire.

6. **Conclusion**:
Therefore, the suitable number of turns for maximum magnetic moment is:
\[ N = 1 \]

### Final Answer:
The suitable number of turns among the options given is **1**.