Magnetic wires simple?

Question

Parallel wire questions always throw me off track. can someone help me figure this out?

Two parallel wires carry currents in opposite directions of I1 = 1.00 A and I2 = 5.10 A. The separation of the wires is 0.11 m. What is the magnetic field strength half way between the wires.

Answer 1

I assume you need the magnitude of the magnetic field (B) and not the actual magnetic field strength (H = B/µo).

If so, use the Biot-Savart Law for parallel wires:  B = (µo * i) / (2 * π * d)

The distance (d) will be 0.11m/2, since you want to find B halfway between the wires; but the 2's will cancel, and it becomes B = (µo * i) / (π * 0.11m).

Solve for B1 using i1 and B2 using i2.  B2 will be larger, so subtract B1 from it (since they are in opposite directions), and you'll get B(net) at the halfway point.

Your answer should be on the order of 10^-5 T.