Physics midterm question: stationary loop near constant current wire

Physics 205B Midterm 2, spring semester 2019
Cuesta College, San Luis Obispo, CA

A square metal loop of resistance R is held stationary near a wire that carries a constant amount of current. Discuss whether or not there will be any induced current in the square metal loop, and explain why. 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. Explains how there would be no induced current in the square loop of wire because:
  1. from RHR2, the direction of current in the straight wire creates a magnetic field at the location of the square loop points into the page, creating a magnetic flux through the square loop that points into the page; and
  2. since the current in the straight wire is constant, the magnetic field it creates at the location of the square loop will have a constant magnitude (along with its constant direction), such that there is a constant, unchanging magnetic flux (magnitude and direction) through the square loop; so
  3. from Faraday's law and Lenz's law, since there is no change in magnetic flux through the square loop, there will be no induced emf and no induced current in the square loop.
  (May instead use RHR1 and discuss how the fictitious positive charges in each segment of the square loop are stationary with respect to the magnetic field of the wire, such that there is no force exerted on them to create an induced current.)
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes:
  4. did not clearly indicate the direction of the magnetic field/flux through the square loop; or
  5. argues that there is no induced current in the square loop because there is no magnetic flux through the square loop (when there is a magnetic flux through the square loop, but it is constant); or
  6. argues that there is an induced current in the square loop even though the magnetic flux through the square loop is constant.
• 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 applying properties 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 systematically 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: midterm02u7aH
p: 14 students
r: 15 students
t: 4 students
v: 3 students
x: 5 students
y: 0 students
z: 0 students

A sample "p" response (from student 0691):
Another sample "p" response (from student 4692):