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

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 Etot 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 Etot there.
  • v:
    Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Misinterprets Etot 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:
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):

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