Physics midterm problem: null electric field location near uneven dipole

Physics 205B Midterm 1, Spring Semester 2010
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 16.35, Multiple-Choice Question 16.10

[20 points.] Consider two point charges held at fixed locations. A –8.0 nC charge is at the origin, and a second +3.5 nC charge is at x = +0.25 m. Determine the location(s) (if any) along the x-axis where the magnitude of the electric field would be zero. (If there are no possible locations, then explain why.) Show your work and explain your reasoning.

Solution and grading rubric:

• p = 20/20:
  Correct. Recognizes that (a) both charges create separate electric fields that must (b) combine to zero somewhere along the x-axis, such that k*|Q_1|/r_1^2 = k*|Q_2|/r_2^2, and (c) substitutes r_1 = x, and r_2 = x - 0.25 m, such that x = +0.74 m (the other solution is x = +0.15 m, which is not physically possible).
  
• r = 16/20:
  Nearly correct, but includes minor math errors. Typically overlooks that distance terms need to be squared, or mangles r_2 substitution in terms of x.
  
• t = 12/20:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Some application of superposition of two separate sources of electric fields.
  
• v = 8/20:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner.
  
• x = 4/20:
  Implementation of ideas, but credit given for effort rather than merit.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
Section 31988
p: 1 student
r: 5 students
t: 2 students
v: 5 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 6686):