The diagram shows three equally spaced wires that are perpendicular to the page.The currents are all equal, two being out of the page and one being into the page.Rank the wires according to the magnitudes of the magnetic forces on them, from least to greatest.
A)1, 2, 3
B)2, then 1 and 3 tie
C)2 and 3 tie, then 1
D)1 and 3 tie, then 2
E)3, 2, 1

Question

The diagram shows three equally spaced wires that are perpendicular to the page.The currents are all equal, two being out of the page and one being into the page.Rank the wires according to the magnitudes of the magnetic forces on them, from least to greatest. 
A)1, 2, 3 
B)2, then 1 and 3 tie 
C)2 and 3 tie, then 1 
D)1 and 3 tie, then 2 
E)3, 2, 1

Quizplus · Accepted Answer

The magnetic force on a wire is given by F = ILB, where I is the current, L is the length of the wire in the magnetic field, and B is the magnetic field strength. Since the currents are all equal and the wires are equally spaced, the length in the magnetic field (B) is also the same for each wire. The direction of the force, however, is determined by the direction of the current and the magnetic field. For wire 1, the magnetic field is up (out of the page) and the current is to the right, so the force is into the page. For wire 2, the magnetic field is up and the current is out of the page, so the force is to the left. For wire 3, the magnetic field is down (into the page) and the current is out of the page, so the force is into the page. Since the magnitudes of the forces are proportional to the current, and the currents are all equal, the ranking of the wires is determined by the directions of the forces. The force on wire 2 is the greatest, since it is perpendicular to both the current and the magnetic field. The forces on wires 1 and 3 are equal in magnitude but opposite in direction, since they are each perpendicular to only one of the current or magnetic field directions. Therefore, wires 1 and 3 tie for second place in terms of the magnitudes of the forces on them.

The Diagram Shows Three Equally Spaced Wires That Are Perpendicular