Three coplanar parallel wires, each carrying a current of 10 A in the same direction, are positioned with a separation of 5.0 cm between consecutive wires. Determine the magnitude of the magnetic force per unit length acting on the wires.

Step-by-step solution

Let the three wires be 1, 2, and 3. The force per unit length between two parallel wires carrying currents I₁ and I₂ separated by a distance r is given by F = ₀ I₁ I₂ 2 r . For the middle wire (wire 2), the forces exerted by wire 1 and wire 3 are equal in magnitude and opposite in direction because the currents and distances are the same. Thus, the net force on the middle wire is zero. For wire 1, both wire 2 and wire 3 exert attractive forces in the same direction. F₁ = F₁₂ + F₁₃ = ₀ I^2 2 d + ₀ I^2 2 (2d) = 3 ₀ I