Physics final exam question: induced current in loops surrounding vertical wire

Physics 205B Final Exam, spring semester 2017
Cuesta College, San Luis Obispo, CA


A vertical wire has a decreasing amount of current flowing upwards. Circular metal loops (of resistance R) oriented flat along the north-south direction are held by four different observers. Determine which observer (if any) will have a coil with an induced counterclockwise current, as seen in this perspective. 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. Determines that only the north observer will experience a counterclockwise induced current, by discussing:
  1. right-hand rule 2, where the thumb runs along a straight current-carrying wire, and fingers curled around the wire give the direction of the magnetic field surrounding the wire; and
  2. from Faraday's law, the east and west observers have coils that will not receive any magnetic flux from the wire's current, so they will not observe any induced current in their coils; while the north and south observers have coils that are oriented to receive the changing magnetic flux from the wire's decreasing current, so they will observe an induced current in their coils; and
  3. from Lenz's law (and right-hand rule 3), only the north observer will experience a counterclockwise induced current to counter the decreasing flux that points east-to-west through it (while the south observer will experience a clockwise induced current to counter the decreasing flux that points west-to-east through it).
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Correctly discusses (1)-(2), but has problems with discussing (3): typically may not have explicitly discussed why the magnetic field of the induced current in the north observer's loop must point in the same direction as the (decreasing) magnetic field from the wire, or determines that the south observer's coil will have a counterclockwise induced current.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. At least some attempt at using magnetic forces and/or magnetic flux. Correctly discusses (1)-(2), but discussion of (3) is incomplete or missing.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at applying theproperties of magnetic fields, forces, motional emf, Faraday's law and Lenz's law.
• x:
  Implementation of ideas, but credit given for effort rather than merit. No clear attempt at applying the 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: finalmR3x
p: 1 student
r: 11 students
t: 2 students
v: 11 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 7117):