Physics final exam question: direction of induced current

Physics 205B Final Exam, spring semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 20.27

The current in a circular loop is decreasing over time. A square metal loop (with a resistance R) is located alongside the circular loop. Discuss why the direction of the induced current in the square metal loop is clockwise. Explain your reasoning using the properties of magnetic fields, magnetic flux, Faraday's law and Lenz's law.

Solution and grading rubric:
  • p:
    Correct. Uses (1) right-hand rules to determine that magnetic flux caused by the circular loop is directed into the page through the square loop; discusses (2) how decreasing current in the circular loop then creates decreasing magnitude flux that points into the page through the square loop; and concludes (3) from Faraday's and Lenz's laws that the changing flux induces a current in the square loop that will supplement the decreasing magnitude flux that points into the page, and thus be clockwise.
  • 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.
  • v:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some attempt at using right-hand rules, magnetic fields, forces, currents, flux, Faraday's (and Lenz's) law, induced emf and induced current.
  • x:
    Implementation/application of ideas, but credit given for effort rather than merit.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
Grading distribution:
Sections 30882, 30883
Exam code: finalEL7a
p: 13 students
r: 4 students
t: 8 students
v: 5 students
x: 5 students
y: 0 students
z: 0 students

A sample "p" response (from student 0115):

A sample "x" response (from student 4297), with at least some rudimentary representation of Lenz's law:

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