Two very long parallel wires in the xy-plane, a distance 2a apart, are parallel to the y-axis and carry equal currents I as shown in the figure. The +z direction points perpendicular to the xy-plane in a right-handed coordinate system. If both currents flow in the +y direction, which one of the graphs shown in the figure below best represents the z component of the net magnetic field, in the xy-plane, as a function of x? (Caution: These graphs are not magnetic field lines.)
A) 1
B) 2
C) 3
D) 4
E) 5

Question

Two very long parallel wires in the xy-plane, a distance 2a apart, are parallel to the y-axis and carry equal currents I as shown in the figure. The +z direction points perpendicular to the xy-plane in a right-handed coordinate system. If both currents flow in the +y direction, which one of the graphs shown in the figure below best represents the z component of the net magnetic field, in the xy-plane, as a function of x? (Caution: These graphs are not magnetic field lines.)  
A) 1 
B) 2 
C) 3 
D) 4 
E) 5

Quizplus · Accepted Answer

Using the right-hand rule, we can determine that the magnetic field lines of each wire will form circles around each wire. When the wires are close together, the circles will overlap, creating a region between the wires with a stronger magnetic field. This is shown in graph 3 where the z-component is largest between x=-a and x=a. The other graphs do not show this behavior, so they can be eliminated.

Two Very Long Parallel Wires in the Xy-Plane, a Distance