Physics midterm question: non-zero total electric field between two charges

Physics 205B Midterm 1, spring semester 2017
Cuesta College, San Luis Obispo, CA

Two point charges are held at fixed locations at x = –2 cm and at x = +2 cm. The charge located at x = –2 cm is negatively charged, and the charge located at x = +2 cm is positively charged. Discuss why it is not possible for the electric field at the origin to be zero, for any possible numerical values (equal or unequal) for these two charges. Explain your reasoning using properties of electric forces, fields, and vector superposition.

Solution and grading rubric:

• p:
  Correct. The (total) electric field magnitude at x = 0 cannot be zero for any possible numerical values for the two source charges, because:
  1. the electric field at x = 0 of the Q₁ source charge points to the left (in towards this negative source charge), and the electric field at x = 0 of the Q₂ source charge also points to the left (out away from this positive source charge), and;
  2. no matter what numerical values the two source charges have, since these two electric field vectors will add at x = 0 (because they point in the same direction, to the left), they cannot possibly cancel each other out.
• r:
  Nearly correct, but includes minor math errors. May not explicitly discuss/demonstrate how the numerical values of the two source charges does not matter.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some garbled attempt at applying properties of electric forces, fields, and vector superposition. May discuss how the two charges attract each other, or has their electric fields pointing pointing in opposite directions at x = 0.
• x:
  Implementation of ideas, but credit given for effort rather than merit. No clear attempt at applying properties of electric forces, fields, and vector superposition.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 30882, 30883
Exam code: midterm01AhC4
p: 9 students
r: 12 students
t: 0 students
v: 9 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 1381):