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

Physics 205B Midterm 2, Fall Semester 2010
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 19.61

[20 points.] Two long straight wires carry different amounts of current in the plane of this page. Determine the direction and magnitude of the magnetic field at the location indicated. 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 B_1 points into the page, and B_2 points out of the page. Finds the magnitudes of these magnetic fields, and since B_2 has a greater magnitude than B_1, the resulting total magnetic field at point P will point out of the page, with a (positive definite) magnitude that is the arithmetic difference of the two magnitudes.
  
• r = 16/20:
  Nearly correct, but includes minor math errors. Direction or magnitude of total magnetic field has minor error.
  
• t = 12/20:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Both direction and magnitude of total magnetic field have minor errors.
  
• v = 8/20:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner.
  
• 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 70856
p: 8 students
r: 1 student
t: 2 students
v: 0 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 8110):