Physics midterm problem: force of two source charges on test charge

Physics 205B Midterm 1, spring semester 2013
Cuesta College, San Luis Obispo, CA

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

Consider two point charges held at fixed locations. A +6.0 nC charge is at x = –1.0 m, and a –8.0 nC charge is at x = +1.5 m. Determine the sign (±) and amount of charge (in either coulombs or nC) to be placed at the origin such that a force of 4.9×10^–8 N directed to the right is exerted on it. If this is not possible, then demonstrate why this is so. Show your work and explain your reasoning.

Solution and grading rubric:

• p:
  Correct. Determines (a) that the charge must be positive in order to be attracted (pulled to the right) by the –8.0 nC charge, and repelled (pushed to the right) by the +6.0 nC charge; and (b) finds the magnitude of the unknown charge, sets up superposition of the two force vectors on the unknown charge add up to 4.9×10^–8 N. May instead find the total electric field E at the position of the unknown test charge from the superposition of the two electric field vectors from each source charge, and then solve for the charge using q = F/E.
• r:
  Nearly correct, but includes minor math errors. At least finds two separate force vectors (or electric field vectors), but typically finds their difference instead of their sum, or only uses the greater vector (force or field) in finding the unknown charge.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Typically only evaluates one of the force vectors on the charge, or one of the electric field vectors at that location to determine the unknown charge.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some constructive attempt at finding the force or electric field to determine the unknown charge.
• x:
  Implementation of ideas, but credit given for effort rather than merit.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Section 30882
Exam code: midterm01p0C4
p: 10 students
r: 7 students
t: 11 students
v: 3 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 7187), using a direct force approach:
Another sample "p" response (from student 1943), instead using a two-step electric field approach: