Two long current-carrying wires are kept parallel at a distance 2r between them and if currents I and 2I respectively are flowing in these in same direction, the resultant magnetic field B at the mid-point between two wires is

Concept Used:

• The magnetic field due to a long straight current-carrying wire at a distance r is given by: B = (μ₀ / 2π) × (I / r)
• At the midpoint between two wires, the distance from each wire is r.
• The net magnetic field is the vector sum of the fields produced by both wires.
• Since the currents flow in the same direction, the magnitude of magnetic fields at the midpoint will subtract using thumb rule.

Here, dot represent the direction of magnetic field into the page and cross represent the direction of magnetic field out of the page

Calculation:

Magnetic field due to the first wire at the midpoint:

B₁ = (μ₀ / 2π) × (I / r)

Magnetic field due to the second wire at the midpoint:

B₂ = (μ₀ / 2π) × (2I / r)

Net magnetic field at the midpoint:

B_net = B₁ - B₂

⇒ B_net = [(μ₀ / 2π) × (I / r)] - [(μ₀ / 2π) × (2I / r)]

∴ B_net = I × (μ₀ / 2πr)

Hence, the correct answer is Option 4: I (μ₀ / 2πr).