The magnetic field at a distance r from a long wire carryimg current I is 0.4 T. The magnetic field at a distance 2r is

Options

A. 0.2 T
B. 0.8 T
C. 0.1 T
D. 1.6 T

Answer

To solve the problem, we need to understand how the magnetic field around a long straight wire carrying current behaves. The magnetic field \( B \) at a distance \( r \) from 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.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- The magnetic field at a distance \( r \) is given as \( B_1 = 0.4 \, T \).
- We need to find the magnetic field \( B_2 \) at a distance \( 2r \).

2. **Understand the Relationship:**
- The magnetic field \( B \) is inversely proportional to the distance \( r \). This means if the distance doubles, the magnetic field will halve.
- Mathematically, we can express this relationship as:
\[ \frac{B_1}{B_2} = \frac{r_2}{r_1} \]

3. **Substitute the Known Values:**
- Here, \( r_1 = r \) and \( r_2 = 2r \).
- Therefore, we can write:
\[ \frac{B_1}{B_2} = \frac{2r}{r} \]
- This simplifies to:
\[ \frac{B_1}{B_2} = 2 \]

4. **Solve for \( B_2 \):**
- Rearranging the equation gives us:
\[ B_2 = \frac{B_1}{2} \]
- Substituting \( B_1 = 0.4 \, T \):
\[ B_2 = \frac{0.4}{2} = 0.2 \, T \]

5. **Conclusion:**
- The magnetic field at a distance \( 2r \) is \( B_2 = 0.2 \, T \).

### Final Answer:
The magnetic field at a distance \( 2r \) is **0.2 T**.