Physics midterm question: comparing total electric field magnitudes

Physics 205B Midterm 1, 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. A +8 nC charge is at the origin, and a second –4 nC charge is at x = +2 cm. The electric field at x = +4 cm is measured. The charge at the origin is then changed to +4 nC, and the electric field at x = +4 cm is again measured. Discuss why the second case has a greater electric field magnitude at x = +4 cm. Explain your reasoning using properties of electric forces, fields, and vector superposition.

Solution and grading rubric:

• p:
  Correct. Discusses/demonstrates that the (total) electric field at x = +4 cm would be greater for the second case (B) using the superposition of the electric field vectors from both source charges (Q₁ = +8 nC and Q₂ = –4 nC for case (A); Q₁ = +4 nC and Q₂ = –4 nC for case (B)), which in both cases point in opposite directions, such that superposition of these vectors is the difference of their magnitudes, and either:
  1. explicitly evaluates the numerical values of the total electric field at x = +4 cm to show that it is indeed greater for the second case (B);
  2. qualitatively discusses how the electric field produced by the Q₁ source charge always points in the opposite direction of, and has a magnitude less than the electric field produced by the Q₂ source charge, such that decreasing the amount of the Q₁ source charge (while keeping its (–) sign) will decrease the amount "subtracted" from the electric field produced by the Q₂ source charge.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. May have a minor computational error, but at least conclusion is consistent with result.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Nearly correct, but argument has conceptual errors, or is incomplete. At least some attempt at evaluating electric fields created by each source charge at x = +4 cm and vector superposition.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Focus on comparing force exerted by source charge Q₁ on source charge Q₂, instead of the comparing effect of electric fields created by source charge Q₁ and source charge Q₂ on x = +4 cm.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Approach other than that of applying electric forces, fields, and vector superposition.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 30882, 30883
Exam code: midterm01p34K
p: 30 students
r: 1 student
t: 3 students
v: 12 students
x: 0 student
y: 0 students
z: 0 student

A sample "p" response (from student 1828):
Another sample "p" response (from student 8984):
A sample "v" response (from student 0203):
A sample "y" response (from student 1212):