Two long, straight, parallel wires separated by a distance d carry currents in opposite directions as shown in the figure. The bottom wire carries a current of 6.0 A. Point C is at the midpoint between the wires and point O is a distance 0.50d below the 6-A wire as suggested in the figure. The total magnetic field at point O is zero tesla.
-Determine the magnitude of the magnetic field at point C if d = 0.10 m.

Question

Two long, straight, parallel wires separated by a distance d carry currents in opposite directions as shown in the figure. The bottom wire carries a current of 6.0 A. Point C is at the midpoint between the wires and point O is a distance 0.50d below the 6-A wire as suggested in the figure. The total magnetic field at point O is zero tesla. 
-Determine the magnitude of the magnetic field at point C if d = 0.10 m.

Quizplus · Accepted Answer

Using the right-hand rule, we can see that the magnetic field due to the bottom wire (6 A) is into the plane of the paper at point O. Since the total magnetic field at point O is zero, the magnetic field due to the top wire (unknown magnitude) must be out of the plane of the paper and have the same magnitude as the magnetic field due to the bottom wire.
At point C, the magnetic field due to the bottom wire is into the plane of the paper and has a magnitude given by:
B1 = μ0(I1/2πd) = 4π × 10^−7 T·m/A × (6.0 A/(2π × 0.10 m)) = 9.55 × 10^−5 T
where μ0 is the magnetic constant (4π × 10^−7 T·m/A).
Therefore, the magnitude of the total magnetic field at point C is:
B = 2B1 = 2 × 9.55 × 10^−5 T ≈ 9.6 × 10^−5 T
which is closest to choice C.

Two Long, Straight, Parallel Wires Separated by a Distance D