Physics midterm problem: total electric field of two fixed source charges

Physics 205B Midterm 1, fall semester 2010
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 16.29

[20 points.] Consider two point charges held at fixed locations. A –8.0 nC charge is at the origin, and a second +3.5 nC charge is at x = +0.20 m. Determine whether the direction of the electric field at x = +0.40 m points to the left or to the right, 
or has no direction (if the electric field magnitude is zero.) Show your work and explain your reasoning.

Solution and grading rubric:
  • p = 20/20:
    Correct. Determines directions of the electric fields of each charge separately at x = +0.40 m, where E-8.0 nC points to the left, and E+3.5 nC points to the right. Finds the magnitudes of these electric fields, and since E+3.5 nC has a greater magnitude than E-8.0 nC, the resulting total electric field at x = +0.40 m will point to the right (with a magnitude that is the arithmetic difference of the two magnitudes).
  • r = 16/20:
    Nearly correct, but includes minor math errors. Does not clearly show the directions for each electric field, or decimal place errors.
  • t = 12/20:
    Nearly correct, but approach has conceptual errors, and/or major/compounded math 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:

Grading distribution:
Section 70856
p: 7 students
r: 3 students
t: 0 students
v: 0 students
x: 0 students
y: 1 student
z: 0 students

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

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