Variation of magnetic field with distance from current carrying conductor is:

Options

A. `B prop a^(2)`
B. `B prop (1)/(a^(2))`
C. `B prop a`
D. `B prop (1)/(a)`

Explanation

To determine the variation of the magnetic field with distance from a current-carrying conductor, we can use Ampere's Law. The magnetic field (B) around a long straight conductor carrying a current (I) is given by the formula:

\[ B = \frac{\mu_0 I}{2 \pi r} \]

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

### Step-by-Step Solution:

1. **Identify the Formula**: The formula for the magnetic field around a straight current-carrying conductor is \( B = \frac{\mu_0 I}{2 \pi r} \).

2. **Understand the Variables**: In this formula:
- \( \mu_0 \) is a constant (permeability of free space),
- \( I \) is the current (which is constant for a given conductor),
- \( r \) is the distance from the conductor, which varies.

3. **Analyze the Relationship**: From the formula, we can see that the magnetic field \( B \) is inversely proportional to the distance \( r \). This means that as you move further away from the conductor (increasing \( r \)), the magnetic field \( B \) decreases.

4. **Conclusion**: Therefore, the variation of the magnetic field with distance from a current-carrying conductor is such that it decreases as the distance increases, following the relationship \( B \propto \frac{1}{r} \).

### Final Statement:
The variation of the magnetic field with distance from a current-carrying conductor is inversely proportional to the distance from the conductor.

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