Physics midterm question: moving loop through opposing magnetic fields

Physics 205B Midterm 2, spring semester 2015
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Example 20.1, Conceptual Example 20.5

A square metal loop of resistance R is dragged from a region with an external magnetic field that points into the plane of this page, to a region with an external magnetic field that points out of the plane of this page. The magnitudes of the magnetic fields in these two regions are the same, only their directions differ. Discuss why the induced current in the loop while it is passing from one region to the other will be clockwise in direction. Explain your reasoning using the properties of magnetic fields, forces, motional emf, Faraday's law and Lenz's law.

Solution and grading rubric:

• p:
  Correct. Discusses/demonstrates that current induced in the square must be clockwise using either (or both) of the following (equivalent) arguments:
  1. right-hand rule 1 to show that the force on fictitious positive charges in the top of the square loop point to the right, while the force on the bottom points to left, resulting in a clockwise flow; or
  2. Faraday's (and Lenz's) law to the changing external magnetic flux through the square loop--as it moves downwards, the flux pointing into the page decreases (while the flux pointing out of the page increases), such that the current induced in the square loop must be clockwise in order to provide a counteracting flux that points into the page.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. At least some attempt at using magnetic forces and/or magnetic flux.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
• x:
  Implementation of ideas, but credit given for effort rather than merit. Approach other than that of applying properties of magnetic fields, forces, motional emf, Faraday's law and Lenz's law.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 30882, 30883
Exam code: midterm02m3tR
p: 31 students
r: 1 student
t: 11 students
v: 4 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 0550), discussing the Lorentz force exerted on fictitious positive charges in the top and bottom segments of the wire loop:
A sample "p" response (from student 8167), using both the Lorentz force, and also applying Lenz's law to the changing flux through the wire loop: