Physics quiz question: two charges exerting forces on each other

Physics 205B Quiz 3, spring semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 16.13

Two point charges 
(+1.6 nC and +3.2 nC) are held a certain distance apart. 
The magnitude of the electric force of the +1.6 nC charge on the +3.2 nC charge is 5.5×10^–5 N. The __________ charge has a greater magnitude electric force exerted on it.
(A) +1.6 nC.
(B) +3.2 nC.
(C) (There is a tie.)
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (C)

These two charges are both positive, such that they will repel each other. Thus the force on the q₁ = +1.6 nC charge points to the left, and the force on the q₂ = +3.2 nC charge points to the right.

The magnitude of the force of the q₁ = +1.6 nC charge on the q₂ = +3.2 nC charge is given by Coulomb's law:

|F_{1 on 2}| = k·|q₁|·|q₂|/(r²),

where r is the center-to-center distance separating these two charges. Likewise the magnitude of the force of the q₂ = +3.2 nC charge on the q₁ = +1.6 nC charge is given by:

|F_{2 on 1}| = k·|q₂|·|q₁|/(r²).

So by inspection of these two equations, these two forces must have the same magnitude.

These two forces are also expected to have the same magnitude, as they satisfy all three components of the POFOSTITO mnemonic (cf. Light and Matter by Benjamin Crowley, lightandmatter.com) form of Newton's third law:

POF: Pair of Opposite Forces (to the left and to the right)
OST: Of Same Type (both electrostatic forces)
ITO: Involving Two Objects (q₁ and q₂)

Thus the force on the q₁ = +1.6 nC charge and the force on the q₂ = +3.2 nC charge are a third law pair, being equal in magnitude and opposite in direction.

Section 30882
Exam code: quiz03F3ld
(A) : 5 students
(B) : 0 students
(C) : 2 students
(D) : 0 students

Success level: 29%
Discrimination index (Aubrecht & Aubrecht, 1983): -0.08