20140511

Physics midterm question: loops at edge of magnetic field region

Physics 205B Midterm 2, spring semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Example 20.1, Problem 20.1

Within a certain region there is an external uniform magnetic field, and the magnetic field is zero everywhere outside of this region. Two square metal loops of the same area, and same resistance R each move with the same constant speed, but in different directions. Discuss why the loop that moves in the +y direction has more induced current than the loop that moves in the +x direction (at the instant both loops are halfway out of the magnetic field region). 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. Applies Faraday's (and Lenz's) law to the changing/constant external magnetic flux through the loops: the upwards moving loop has a changing (decreasing) external magnetic flux through it, so it will have an induced current in it; while the loop moving to the right will have a constant external magnetic flux, so there is not induced current in it. Or may argue using right-hand rule 1 to show that the upwards loop will have a net clockwise current due to the magnetic force on fictitious positive charges in its bottom section, while the loop moving to the right will not have a net current due to the magnetic force on the fictitious positive charges on its side sections both pointing upwards.
  • 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 of ideas, but credit given for effort rather than merit.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
    Blank.
Grading distribution:
Sections 30882, 30883
Exam code: midterm02iF47
p: 27 students
r: 7 students
t: 5 students
v: 1 student
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 0007), with a graphical approach to Faraday's and Lenz's laws:

Another sample "p" response (from student 7979), instead discussing the effect of magnetic forces on the fictitious positive charges in the loops:

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