The magnetic field at a perpendicular distance of `2cm` from an infinite straight current carrying conductor is `2xx10^-6T`. The current in the wire is

Options

A. `0*1A`
B. `0*2A`
C. `0*4A`
D. `0*8A`

Answer

To find the current in the wire given the magnetic field at a perpendicular distance from an infinite straight current-carrying conductor, we can follow these steps:

### Step-by-Step Solution:

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

2. **Identify Given Values**:
- Magnetic field \( B = 2 \times 10^{-6} \, \text{T} \)
- Distance \( d = 2 \, \text{cm} = 0.02 \, \text{m} \)

3. **Rearrange the Formula to Solve for Current \( I \)**:
Rearranging the formula for \( I \):
\[ I = \frac{B \cdot 2 \pi d}{\mu_0} \]

4. **Substitute the Known Values**:
Substitute \( B \), \( d \), and \( \mu_0 \) into the equation:
\[ I = \frac{(2 \times 10^{-6} \, \text{T}) \cdot (2 \pi \cdot 0.02 \, \text{m})}{4\pi \times 10^{-7} \, \text{T m/A}} \]

5. **Calculate the Current**:
Simplifying the equation:
\[ I = \frac{(2 \times 10^{-6}) \cdot (0.04 \pi)}{4\pi \times 10^{-7}} \]
The \( \pi \) cancels out:
\[ I = \frac{(2 \times 10^{-6}) \cdot 0.04}{4 \times 10^{-7}} = \frac{8 \times 10^{-8}}{4 \times 10^{-7}} = 0.2 \, \text{A} \]

6. **Final Answer**:
The current in the wire is:
\[ I = 0.2 \, \text{A} \]