Two long parallel wires are separated by a distance d and carry equal currents I in opposite directi

Question

Two long parallel wires are separated by a distance d and carry equal currents I in opposite directions. What is the magnitude of the magnetic field midway between them?

Professor PC Thomas Classes · Answer

Field due to each wire at the midpoint ($d/2$) is $B_1 = B_2 = \frac{\mu_0 I}{2\pi (d/2)} = \frac{\mu_0 I}{\pi d}$. Since currents are in opposite directions, the fields add up: $B_{net} = \frac{2\mu_0 I}{\pi d}$.