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 the left current flows in the +y direction and the right current flows 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 the left current flows in the +y direction and the right current flows 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 around each current are traveling in the counterclockwise direction. Therefore, on the left side of the two wires, the magnetic field lines will be pointing into the plane (toward negative z) and on the right side, they will be pointing out of the plane (toward positive z).

In choice D, we see a graph that has a negative value on the left side of the origin and a positive value on the right side of the origin, which matches our expectation for the magnetic field direction. The magnitude of the magnetic field should decrease with increasing distance from the wires, so we also see that the graph approaches zero as we move further away from the wires.

Therefore, choice D is the best representation of the z component of the net magnetic field in the xy-plane.

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