20160327

Physics midterm problem: comparing total electric field magnitudes

Physics 205B Midterm 1, spring semester 2016
Cuesta College, San Luis Obispo, CA

Two point charges are held at fixed locations. A +5 nC charge is at the origin, and a second –1 nC charge is at x = +4 cm. Discuss why the magnitude of the electric field at x = +2 cm is less than the magnitude of the electric field at x = +3 cm. Show your work and 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 magnitude would be greater at x = +3 cm than at x = +2 cm by:
    1. evaluating the individual electric field magnitudes E1 and E2 created by the source charges Q1 and Q2 at each location (four separate terms), and;
    2. discussing how for each location the individual electric field magnitudes add together, as they both point in the same direction to the right (away from Q1 = +5 nC, and in towards Q2 = −1 nC), and;
    3. either completely evaluating the total electric field magnitude at each location, or comparing their values in terms of in common relative terms of k, nC, and cm2.
  • 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. At least some attempt at evaluating electric fields created by each source charge at both locations and vector superposition.
  • v:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at applying electric forces, fields, and vector superposition.
  • x:
    Implementation/application 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: midterm01rx1C
p: 22 students
r: 7 students
t: 8 students
v: 4 students
x: 2 student
y: 0 students
z: 0 student

A sample "p" response (from student 0001), explicitly evaluating the electric field magnitudes:

A sample "p" response (from student 0720), eliminating common factors:
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