Physics midterm problem: total magnetic field of two current-carrying wires

Physics 205B Midterm 2, spring semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 19.71

[20 points.] Two long straight wires carry currents of equal magnitude, but heading in opposite directions. The wires are shown perpendicular to the plane of this page. The magnetic field at point P has a magnitude and direction of 1.3×10^–6 T in the +y direction. Calculate the amount of current in wire 2, and its direction. Show your work and explain your reasoning.

Solution and grading rubric:

• p = 20/20:
  Correct. Determines directions of the magnetic fields of each current separately at point P, where B₂ (larger in magnitude, generated by the nearer I₂ current) points up, and B₁ points down, such that I₂ must point out of the page (and I₁ points into the page). Then finds the magnitude of the currents by equating the total magnetic field magnitude to the arithmetic difference of the magnitudes of the two magnetic fields generated by I₁ and I₂.
  
• r = 16/20:
  Nearly correct, but includes minor math errors.
  
• t = 12/20:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Equates the total magnetic field magnitude to the arithmetic sum of the magnitudes of the two magnetic fields generated by I₁ and I₂.
  
• v = 8/20:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. As (t), but explanation of I₂ current direction incorrect or missing; or sets total magnetic field magnitude equal to the magnetic field generated by I₂ only.
  
• x = 4/20:
  Implementation of ideas, but credit given for effort rather than merit.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
Section 30882
Exam code: midterm02B1rD
p: 7 students
r: 2 students
t: 4 students
v: 13 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 3389):