Magnetic field at a distance r from an infinitely long straight conductor carrying steady varies as

Options

A. `1//r^(2)`
B. `1//r`
C. `1//r^(2)`
D. `1//sqrtr`

Explanation

To find how the magnetic field varies at a distance \( r \) from an infinitely long straight conductor carrying a steady current, we can follow these steps:

### Step-by-Step Solution

1. **Understand the Setup**:
We have an infinitely long straight conductor carrying a steady current \( I \). We want to determine the magnetic field \( B \) at a distance \( r \) from the conductor.

2. **Use Ampère's Law**:
According to Ampère's Law, the magnetic field around a long straight conductor can be calculated using the formula:
\[ B = \frac{\mu_0 I}{2 \pi r} \]
where \( \mu_0 \) is the permeability of free space.

3. **Identify the Variables**:
Here, \( B \) is the magnetic field, \( I \) is the current flowing through the conductor, and \( r \) is the distance from the conductor.

4. **Analyze the Formula**:
From the formula \( B = \frac{\mu_0 I}{2 \pi r} \), we can see that the magnetic field \( B \) is inversely proportional to the distance \( r \). This means that as the distance \( r \) increases, the magnetic field \( B \) decreases.

5. **Conclusion**:
Therefore, we can conclude that the magnetic field \( B \) at a distance \( r \) from an infinitely long straight conductor varies inversely with \( r \):
\[ B \propto \frac{1}{r} \]

### Final Answer
The magnetic field at a distance \( r \) from an infinitely long straight conductor carrying a steady current varies as \( \frac{1}{r} \).

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