A current of 5A flows downwards in a long straight vertical conductor and the earth's horizontal flux density is `2xx10^(-7)T` then the neutral point occurs

Options

A. due north 10 cm from the wire
B. due east 10m from the wire
C. due east 5m from the wire
D. due west 5m from the wire

Answer

To solve the problem, we need to find the distance from the vertical conductor to the neutral point where the magnetic field due to the current in the conductor is equal in magnitude but opposite in direction to the Earth's horizontal magnetic flux density.

### Step-by-Step Solution:

1. **Identify Given Data:**
- Current (I) flowing in the conductor = 5 A
- Earth's horizontal flux density (B_E) = \(2 \times 10^{-7} \, \text{T}\)

2. **Understand the Concept of Neutral Point:**
- The neutral point is where the magnetic field due to the conductor cancels out the Earth's magnetic field. Mathematically, this can be expressed as:
\[ B_{\text{conductor}} = B_E \]
- The direction of \(B_{\text{conductor}}\) will be opposite to that of \(B_E\).

3. **Formula for Magnetic Field Due to a Long Straight Conductor:**
- The magnetic field (B) at a distance (r) from a long straight conductor carrying current I is given by:
\[ B = \frac{\mu_0 I}{2 \pi r} \]
- Where \(\mu_0\) (the permeability of free space) is approximately \(4\pi \times 10^{-7} \, \text{T m/A}\).

4. **Set Up the Equation:**
- At the neutral point:
\[ \frac{\mu_0 I}{2 \pi r} = B_E \]
- Substitute the values:
\[ \frac{4\pi \times 10^{-7} \times 5}{2 \pi r} = 2 \times 10^{-7} \]

5. **Simplify the Equation:**
- Cancel \(\pi\) from both sides:
\[ \frac{4 \times 10^{-7} \times 5}{2r} = 2 \times 10^{-7} \]
- This simplifies to:
\[ \frac{20 \times 10^{-7}}{2r} = 2 \times 10^{-7} \]
- Further simplifying gives:
\[ \frac{10 \times 10^{-7}}{r} = 2 \times 10^{-7} \]

6. **Solve for r:**
- Cross-multiply to solve for r:
\[ 10 \times 10^{-7} = 2 \times 10^{-7} r \]
- Dividing both sides by \(2 \times 10^{-7}\):
\[ r = \frac{10 \times 10^{-7}}{2 \times 10^{-7}} = 5 \, \text{m} \]

7. **Conclusion:**
- The neutral point occurs at a distance of 5 meters from the wire in the east direction.

### Final Answer:
The neutral point occurs at a distance of **5 meters** from the wire.