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 students

A sample "p" response (from student 0001), explicitly evaluating the electric field magnitudes:
A sample "p" response (from student 0720), eliminating common factors:>