Physics quiz question: finding amount of unknown charge

Physics 205B Quiz 3, spring semester 2020
Cuesta College, San Luis Obispo, CA

A –4.5 nC point charge and an unknown positive point charge are held a distance of 3.0 cm apart. The magnitude of the electric force of the –4.5 nC charge on the unknown positive charge is 7.6×10^–5 N. The amount of the unknown positive charge is:
(A) 1.7×10^–9 C.
(B) 5.6×10^–8 C
(C) 1.7×10⁴ C.
(D) 4.5×10⁴ C.

Correct answer (highlight to unhide): (A)

The magnitude of the force on the unknown positive point charge is given by:

|F_{1 on 2}| = k·|q₁|·|q₂|/(r²),

where q₁ is the –4.5 nC point charge, and q₂ is the unknown positive charge. Then the absolute value of the unknown charge can then be solved for:

|q₂| = |F_{1 on 2}|·(r²)/(k·|q₁|),

|q₁| = |7.6×10^–5 N|·(0.030 m)²/((8.99×10⁹ N·m²/C²)·|–4.4×10^–9 C|),

|q₁| = 1.6907675195...×10^–9 C,

or to two significant figures, the amount of the unknown (positive) charge is (+)1.7×10^–9 C.

(Response (B) is |F_{1 on 2}|·r/(k·|q₁|); response (C) is |F_{1 on 2}|/|q₁| (which is the electric field of the unknown positive charge at the location of the –4.5 nC charge); and response (D) is k·|q₁|/r² (which is the electric field of the –4.5 nC charge at the location of the unknown positive charge).)

Sections 30882, 30883
Exam code: quiz03Cv1d
(A) : 28 students
(B) : 1 student
(C) : 4 students
(D) : 1 student

Success level: 82%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.18