A straight wire of diameter 1 mm carries a current of 1A. It is replaced by another wire of diameter 2 MM, carrying same current . The strength of the magnetic field :

Options

A. Twice the former value
B. One half of the former value
C. Same as the former value
D. One quarter of the former value

Answer

To solve the problem, we need to determine how the strength of the magnetic field changes when a straight wire of diameter 1 mm carrying a current of 1 A is replaced by another wire of diameter 2 mm, while maintaining the same current.

### Step-by-Step Solution:

1. **Understand the Magnetic Field Formula**:
The magnetic field (B) around a long straight wire carrying current (I) is given by the formula:
\[ B = \frac{\mu_0 I}{2 \pi r} \]
where \( \mu_0 \) is the permeability of free space and \( r \) is the distance from the center of the wire to the point where the magnetic field is being measured.

2. **Identify the Parameters**:
- Current (I) = 1 A (same for both wires)
- Diameter of the first wire = 1 mm
- Diameter of the second wire = 2 mm

3. **Determine the Distance (r)**:
The distance \( r \) is measured from the center of the wire to the point where we are calculating the magnetic field. Since the question does not specify the distance from the wire to the point of measurement, we will assume that it remains constant for both wires.

4. **Analyze the Effect of Diameter**:
The formula for the magnetic field does not include the diameter of the wire. It only depends on the current and the distance from the wire. Therefore, changing the diameter of the wire does not affect the magnetic field strength at a given distance \( r \).

5. **Conclusion**:
Since the magnetic field strength depends only on the current and the distance from the wire, and since both wires carry the same current and we assume the distance remains unchanged, the magnetic field strength remains the same.

Thus, the strength of the magnetic field when the wire is replaced will be the same as the former value.

### Final Answer:
The strength of the magnetic field remains the same as the former value.