To solve this problem, we need to find the magnetic field strength at the midpoint between two long straight wires carrying current in the same direction.
### Step 1: Magnetic field due to a single wire
The magnetic field at a distance \( r \) from a long straight wire carrying a current \( i \) is given by Ampère's law:
\[ B = \frac{\mu_0 i}{2 \pi r} \]
where:
- \( \mu_0 \) is the permeability of free space,
- \( i \) is the current in the wire,
- \( r \) is the distance from the wire.
### Step 2: Consider the two wires
Let the two wires be separated by a distance \( r \). The magnetic field at the midpoint between the wires will be due to the fields created by both wires.
- For each wire, the magnetic field at the midpoint will have the same magnitude, but their directions will differ.
- Since both wires carry current in the same direction, the magnetic field due to each wire will be in opposite directions at the midpoint (due to the right-hand rule).
### Step 3: Combine the magnetic fields
At the midpoint, the magnetic fields due to the two wires will add up because they are in the same direction (since the currents are in the same direction). The total magnetic field at the midpoint is the sum of the magnetic fields due to both wires.
For each wire, the magnetic field at the midpoint is:
\[ B_{\text{wire}} = \frac{\mu_0 i}{2 \pi r/2} = \frac{\mu_0 i}{\pi r} \]
Since there are two wires, the total magnetic field at the midpoint is:
\[ B_{\text{total}} = 2 \times \frac{\mu_0 i}{\pi r} = \frac{2 \mu_0 i}{\pi r} \]
### Final Answer:
The strength of the magnetic field at the midpoint is:
\[ \boxed{\frac{2 \mu_0 i}{\pi r}} \]
So, the correct answer is **B**.
