To solve the problem step by step, we need to find the distance of point P from either of the wires. Let's denote the distance from each wire to point P as \( d \). The distance between the two wires is given as 1 meter, so if the distance from one wire to point P is \( d \), then the distance from the other wire to point P will be \( 1 - d \).
### Step 1: Understanding the Magnetic Field Contribution
The magnetic field \( B \) due to a long straight wire carrying current \( I \) at a distance \( d \) from the wire is given by the formula:
\[
B = \frac{\mu_0 I}{2 \pi d}
\]
where \( \mu_0 \) is the permeability of free space, given as \( 4 \pi \times 10^{-7} \, \text{T m/A} \).
### Step 2: Magnetic Field at Point P
Since both wires carry the same current \( I = 1 \, \text{A} \) in the same direction, the magnetic fields due to both wires at point P will add up. The total magnetic field \( B_P \) at point P, which is equidistant from both wires, can be expressed as:
\[
B_P = B_1 + B_2 = 2B
\]
Thus, substituting the expression for \( B \):
\[
B_P = 2 \left( \frac{\mu_0 I}{2 \pi d} \right) = \frac{\mu_0 I}{\pi d}
\]
### Step 3: Setting Up the Equation
We know from the problem statement that the magnetic field intensity at point P is given as:
\[
B_P = 1.6 \times 10^{-7} \, \text{T}
\]
Equating the two expressions for \( B_P \):
\[
\frac{\mu_0 I}{\pi d} = 1.6 \times 10^{-7}
\]
### Step 4: Substituting Known Values
Substituting \( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \) and \( I = 1 \, \text{A} \):
\[
\frac{4 \pi \times 10^{-7} \times 1}{\pi d} = 1.6 \times 10^{-7}
\]
This simplifies to:
\[
\frac{4 \times 10^{-7}}{d} = 1.6 \times 10^{-7}
\]
### Step 5: Solving for \( d \)
Rearranging the equation to solve for \( d \):
\[
d = \frac{4 \times 10^{-7}}{1.6 \times 10^{-7}} = \frac{4}{1.6} = 2.5 \, \text{m}
\]
### Step 6: Finding the Correct Distance
Since the distance between the two wires is 1 meter, the maximum distance \( d \) cannot exceed 1 meter. Thus, we need to find the correct distance \( d \) that satisfies the geometry of the problem.
### Step 7: Using Geometry
Given that the point P is equidistant from both wires, we can denote the distance from each wire to point P as \( d \) and the distance between the wires as \( 1 \, \text{m} \). Using the right triangle formed by the wires and point P, we can set up the equation:
\[
d + d = 1 \implies d = 0.5 \, \text{m}
\]
### Final Answer
Thus, the distance of point P from either of the wires is:
\[
\boxed{0.5 \, \text{m}}
\]
