Physics quiz question: finding amount of unknown charge

Physics 205B Quiz 3, spring semester 2014
Cuesta College, San Luis Obispo, CA

Two point charges are held at fixed positions. The –4.0 µC point charge at x = +1.5 m experiences 
a force directed to the right with a magnitude of 2.1×10^–4 N. The point charge at the origin is:
(A) –1.3×10^–8 C.
(B) –8.8×10^–9 C.
(C) –5.3×10^–14 C.
(D) +5.3×10^–14 C.
(E) +8.8×10^–9 C.
(F) +1.3×10^–8 C.

Correct answer (highlight to unhide): (A)

The force on the –4.0 µC charge at x = +1.5 m points to the right, such that it is being repelled by the unknown charge at the origin. This means that the charge at the origin must also be a negative charge, as like charges repel.

The magnitude of the force on the –4.0 nC charge at x = +1.5 m is given by:

|F_{1 on 2}| = k·|q₁|·|q₂|/(r²),

where q₁ is the unknown charge at the origin, and q₂ is the charge at x = +1.5 m. Then the absolute value of the unknown charge can then be solved for:

|q₁| = |F_{1 on 2}|·(r²)/(k·|q₂|),

|q₁| = |2.1×10^–4 N|·(1.5 m)²/((8.99×10⁹ N·m²/C²)·|–4.0×10^–6 C|),

|q₁| = 1.3139599555...×10^–8 C.

As discussed above, this charge is expected to be negative, such that to two significant figures the charge at the origin is –1.3×10^–8 C.

(Response (B) is |F_{1 on 2}|·r/(k·|q₂|); response (C) is |F_{1 on 2}|·(r²)/k; responses (D)-(F) all have the wrong sign.)

Sections 30882, 30883
Exam code: quiz03cDvD
(A) : 22 students
(B) : 4 students
(C) : 4 students
(D) : 4 students
(E) : 0 students
(F) : 6 students

Success level: 55%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.66