The magnetic flux density at a point distant d from a long straight current carrying conductor is B, then its value at distance `d/2` will be-

Options

A. 4B
B. 2B
C. `B/2`
D. `B/4`

Explanation

To solve the problem of finding the magnetic flux density at a distance \( \frac{d}{2} \) from a long straight current-carrying conductor, we can use the formula for the magnetic field around a long straight conductor, which is given by:

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

where:
- \( B \) is the magnetic flux density,
- \( \mu_0 \) is the permeability of free space,
- \( I \) is the current flowing through the conductor,
- \( d \) is the distance from the conductor.

### Step-by-Step Solution:

1. **Identify the formula for magnetic flux density**:
The magnetic flux density \( B \) at a distance \( d \) from a long straight conductor is given by:
\[ B = \frac{\mu_0 I}{2 \pi d} \]

2. **Substitute the distance \( d \) with \( \frac{d}{2} \)**:
We need to find the magnetic flux density at a distance \( \frac{d}{2} \):
\[ B' = \frac{\mu_0 I}{2 \pi \left(\frac{d}{2}\right)} \]

3. **Simplify the expression**:
When we simplify the equation, we get:
\[ B' = \frac{\mu_0 I}{2 \pi \cdot \frac{d}{2}} = \frac{\mu_0 I}{\pi d} \]

4. **Relate \( B' \) to \( B \)**:
We can relate \( B' \) to the original magnetic flux density \( B \):
\[ B' = 2 \cdot \frac{\mu_0 I}{2 \pi d} = 2B \]

5. **Conclusion**:
Therefore, the magnetic flux density at a distance \( \frac{d}{2} \) from the conductor is:
\[ B' = 2B \]

### Final Answer:
The value of the magnetic flux density at a distance \( \frac{d}{2} \) is \( 2B \).