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

Physics 205B Midterm 1, spring semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Multiple-Choice Question 16.10, Problem 16.35

[20 points.] Consider two point charges held at fixed locations. A –7.0 nC charge is at the origin, and a second charge (of unknown sign and amount) is at x = +0.20 m. Determine the sign (±) and amount of charge (coulombs or nC) of the second charge such the electric field is zero at x = +0.50 m. If instead this is not possible, then demonstrate why this is so. Show your work and explain your reasoning.

Solution and grading rubric:
  • p = 20/20:
    Correct. Sets electric field of -7.0 nC charge at x = +0.50 m equal in magnitude to electric field of unknown charge at that same location. Finds magnitudes of the unknown charge, and also explicitly explains that the sign of the unknown charge must be positive.
  • r = 16/20:
    Nearly correct, but includes minor math errors. Determination of positive sign of the unknown charge is not explained, or is negative; or explains positive sign of charge, but minor algebraic or computational errors.
  • t = 12/20:
    Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Missing explanation of positive sign of charge, and minor computational errors.
  • v = 8/20:
    Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some attempt at finding the electric field magnitude of the -7.0 nC charge, or explaining that the unknown charge must be positive.
  • x = 4/20:
    Implementation of ideas, but credit given for effort rather than merit. Use of force, electric potential, etc.
  • y = 2/20:
    Irrelevant discussion/effectively blank.
  • z = 0/20:

Grading distribution:
Section 30882
Exam code: midterm01o1Ls
p: 6 students
r: 10 students
t: 1 student
v: 4 students
x: 6 students
y: 0 students
z: 0 students

A sample "p" response (from student 4027):

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