What is the current in a straight wire, if a magnetic field of `10^(-6)W//m^(2)` is produced at a distance of 2 cm from it ?

Options

A. `0.1A`
B. `0.2A`
C. `0.5A`
D. `0.4A`

Explanation

To find the current in a straight wire that produces a magnetic field of \(10^{-6} \, \text{W/m}^2\) at a distance of 2 cm from it, we can use the formula for the magnetic field around a long straight conductor:

\[ B = \frac{\mu_0}{4\pi} \cdot \frac{2I}{d} \]

where:
- \(B\) is the magnetic field,
- \(I\) is the current,
- \(d\) is the distance from the wire,
- \(\mu_0\) is the permeability of free space, approximately \(4\pi \times 10^{-7} \, \text{T m/A}\).

### Step-by-step Solution:

1. **Convert the distance from cm to m**:
\[ d = 2 \, \text{cm} = 0.02 \, \text{m} \]

2. **Use the formula for the magnetic field**:
\[ B = \frac{\mu_0}{4\pi} \cdot \frac{2I}{d} \]

3. **Substitute the known values into the formula**:
We know \(B = 10^{-6} \, \text{W/m}^2\) and \(\mu_0 = 4\pi \times 10^{-7} \, \text{T m/A}\):
\[ 10^{-6} = \frac{(4\pi \times 10^{-7})}{4\pi} \cdot \frac{2I}{0.02} \]
Simplifying gives:
\[ 10^{-6} = 10^{-7} \cdot \frac{2I}{0.02} \]

4. **Rearranging the equation to solve for \(I\)**:
\[ 10^{-6} = 10^{-7} \cdot \frac{2I}{0.02} \]
Multiply both sides by \(0.02\):
\[ 0.02 \cdot 10^{-6} = 10^{-7} \cdot 2I \]
\[ 2I = \frac{0.02 \cdot 10^{-6}}{10^{-7}} \]
\[ 2I = 0.02 \cdot 10^{1} = 0.2 \]
\[ I = \frac{0.2}{2} = 0.1 \, \text{A} \]

5. **Final answer**:
The current in the straight wire is:
\[ I = 0.1 \, \text{A} \]