20200312

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:

|F1 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| = |F1 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 |F1 on 2r/(k·|q1|); response (C) is |F1 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

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