In a wire of circular form has 4A current is following to have a magnetic induction as `1μT` , at its centre. The radius of circle should be approximately

Options

A. 2.5 m
B. 2.5 cm
C. 2.5 mm
D. 25 cm

Answer

To solve the problem of finding the radius of a circular wire carrying a current of 4 A that produces a magnetic induction of 1 μT at its center, we can use the formula for the magnetic field at the center of a circular loop of wire.

### Step-by-step Solution:

1. **Understand the Formula**: The magnetic field (B) at the center of a circular loop of radius R carrying a current I is given by the formula:
\[ B = \frac{\mu_0 \cdot I}{2 \cdot R} \]
where \( \mu_0 \) is the permeability of free space, approximately \( 4\pi \times 10^{-7} \, \text{T m/A} \).

2. **Rearrange the Formula**: We need to find the radius \( R \). Rearranging the formula gives:
\[ R = \frac{\mu_0 \cdot I}{2 \cdot B} \]

3. **Substitute the Values**: We know:
- \( I = 4 \, \text{A} \)
- \( B = 1 \, \mu\text{T} = 1 \times 10^{-6} \, \text{T} \)
- \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m/A} \)

Substituting these values into the rearranged formula:
\[ R = \frac{(4\pi \times 10^{-7}) \cdot 4}{2 \cdot (1 \times 10^{-6})} \]

4. **Calculate the Numerator**:
\[ 4\pi \times 10^{-7} \cdot 4 = 16\pi \times 10^{-7} \, \text{T m/A} \]

5. **Calculate the Denominator**:
\[ 2 \cdot (1 \times 10^{-6}) = 2 \times 10^{-6} \, \text{T} \]

6. **Combine the Results**: Now substituting back into the equation for R:
\[ R = \frac{16\pi \times 10^{-7}}{2 \times 10^{-6}} = \frac{16\pi}{2} \times 10^{-1} = 8\pi \times 10^{-1} \, \text{m} \]

7. **Calculate the Value**: Using \( \pi \approx 3.14 \):
\[ R \approx 8 \cdot 3.14 \times 10^{-1} = 25.12 \times 10^{-1} \, \text{m} = 2.512 \, \text{m} \]

8. **Final Answer**: Rounding off, we get:
\[ R \approx 2.5 \, \text{m} \]

### Conclusion:
The radius of the circular wire should be approximately **2.5 meters**.