A straight wilre of diameter `0.5 mm` carrying a current `2A` is replaced by another wire of diameter `1 mm` carrying the same current. The strength of magnetic field at a distance `2 m` away from the centre is

Options

A. half of the previous value
B. twice of the previous value
C. unchanged
D. quarter of its previous value

Explanation

To solve the problem, we need to calculate the magnetic field strength at a distance of 2 meters from the center of a straight wire carrying a current. The key points to note are that the current remains the same in both wires, and the diameter of the wire does not affect the magnetic field strength at a given distance.

### Step-by-Step Solution:

1. **Identify the Formula for Magnetic Field**:
The magnetic field \( B \) at a distance \( A \) from a long straight wire carrying a current \( I \) is given by the formula:
\[ B = \frac{\mu_0 I}{2 \pi A} \]
where \( \mu_0 \) is the permeability of free space, approximately \( 4\pi \times 10^{-7} \, \text{T m/A} \).

2. **Determine the Given Values**:
- Current \( I = 2 \, \text{A} \)
- Distance \( A = 2 \, \text{m} \)

3. **Substitute the Values into the Formula**:
Plugging in the values into the formula:
\[ B = \frac{(4\pi \times 10^{-7} \, \text{T m/A}) \times (2 \, \text{A})}{2 \pi (2 \, \text{m})} \]

4. **Simplify the Expression**:
The \( 2\pi \) in the numerator and denominator cancels out:
\[ B = \frac{4 \times 10^{-7} \times 2}{2 \times 2} = \frac{4 \times 10^{-7}}{2} = 2 \times 10^{-7} \, \text{T} \]

5. **Conclusion**:
The strength of the magnetic field at a distance of 2 meters from the center of the wire is:
\[ B = 2 \times 10^{-7} \, \text{T} \]

### Final Answer:
The strength of the magnetic field at a distance of 2 meters from the center of the wire is \( 2 \times 10^{-7} \, \text{T} \).