Physics final exam question: total magnetic field of two current-carrying wires

Physics 205B Final Exam, spring semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 19.61, 19.71

Two long straight wires carry currents, both outwards perpendicular to the plane of this page. Determine the direction of the total magnetic field at the location x = +3.0 cm. Explain your answer using the properties of currents, magnetic fields, and superposition.

Solution and grading rubric:

• p:
  Correct. At x = +3.0 cm, magnetic field of 0.080 A wire points upwards and has a larger magnitude, while magnetic field of 0.020 A wire points downwards and has a smaller magnitude, such that the total magnetic field at that location points upwards.
  
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Chooses stronger magnetic field contribution to determine direction of total magnetic field.
  
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Calculates magnitudes of each magnetic field contribution at x = +3.0 cm, but garbles directions and/or superposition.
  
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
  
• x:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
Section 30882
Exam code: finalsM0k
p: 16 students
r: 1 student
t: 3 students
v: 2 students
x: 1 student
y: 1 student
z: 0 students

A sample "p" response (from student 0524):
Another sample "p" response (from student 1227):