Physics final exam problem: unknown charge contributing to total electric field

Physics 205B Final Exam, spring semester 2015
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 16.15

Two point charges are held at fixed locations. An unknown charge is at the origin, and a –4.0 µC charge is at x = +0.20 m. The electric field at x = +0.10 m points to the right and has a magnitude of 1.8✕10⁵ N/C. Determine the sign (±) and amount of the unknown charge (in either coulombs or µC) that is located at the origin. Show your work and explain your reasoning using properties of electric forces, fields, and vector superposition.

Solution and grading rubric:

• p:
  Correct. Determines that:
  1. the electric field E₁ at x = +0.10 m due to the Q₁ = 4.0 μC charge at x = +0.20 m points to the right, but is more than the total electric field E_tot at x = +0.10 m (that points to the right), thus the electric field E₂ at x = +0.10 m due to the Q₂ charge at the origin must point to the left, and so the charge Q₂ must be negative as well;
  2. from setting up vector superposition of the two oppositely directed electric fields E₁ and E₂ at x = +0.10 m, that the Q₂ charge at the origin must be –3.8 μC.
• r:
  Nearly correct, but includes minor math errors.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least recognizes that there is superposition of two electric fields at x = +0.10 m that result in the given E_tot there.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Misinterprets E_tot at x = +0.10 m m to be the electric force exerted by Q₁ on Q₂, and then solves for Q₁ from Coulomb's law.
• x:
  Implementation of ideas, but credit given for effort rather than merit. No clear attempt at applying electric forces, fields, and vector superposition.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 30882, 30883
Exam code: finalLd0c
p: 3 students
r: 2 students
t: 8 students
v: 19 students
x: 4 student
y: 3 students
z: 4 student

A sample "p" response (from student 8282):
A sample "v" response (from student 9224):