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:
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):

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