Physics midterm problem: total electric field direction to the side of two charges

Physics 205B Midterm 1, spring semester 2019
Cuesta College, San Luis Obispo, CA

A –3.0 nC point charge is held at the origin, and +2.0 nC point charge is held at x = +1 cm. Discuss why the electric field at x = +2 cm is directed to the right. 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 = +2 cm would point to the right by:
  1. calculating or comparing the individual electric field magnitudes for E₂ (larger magnitude, 1.8×10⁵ N/C) and E₁ (smaller magnitude, 6.8×10⁴ N/C) created by the source charges Q₁ and Q₂ at x = +2 cm; and
  2. determining the individual electric field directions for E₁ (to the right, out away from the positive Q₁ source charge) and E₂ (to the left, in towards the negative Q₂ source charge) at x = +2 cm; and
  3. explaining that the vector superposition of E₁ and E₂ at x = +2 cm will result in a total electric field that points to the right, as it (a) will have the direction of the larger of two opposite electric field vectors there, or (b) would be the result of the subtraction of a smaller E₁ magnitude (to the left) from the larger E₂ magnitude (to the right).
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least some attempt at finding electric field magnitudes and directions created by each source charge at x = +2 cm, and discusses result of the addition of these electric field vectors.
• 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. Typically discusses the force that these charges exert on each other.
• 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: midterm01Ft6G
p: 24 students
r: 3 students
t: 6 students
v: 7 students
x: 0 students
y: 0 students
z: 2 students

A sample "p" response (from student 1810):
Another sample "p" response (from student 7843), being more explicit about the different directions of the individual electric fields:
And another sample "p" response (from student 1982), ignoring the common factor of k, and nC and cm unit conversions for purposes of comparison: