Physics quiz question: separation distance between two point charges

Physics 205B Quiz 3, fall semester 2010
Cuesta College, San Luis Obispo, CA

Two point charges 
(–2.5 nC and +3.0 nC) are held a certain distance apart. 
The magnitude of the electric force of the –2.5 nC charge on the +3.0 nC charge is 1.8×10^–6 N. The distance between these charges is:
(A) 2.0×10⁶ m.
(B) 0.037 m.
(C) 0.050 m.
(D) 0.19 m.

Correct answer (highlight to unhide): (D)

The magnitude of the force of the q₁ = –2.5 nC charge on the q₂ = +3.0 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, and can be given by:

r = √(k·|q₁|·|q₂|/|F_{1 on 2}|),

r = √(8.99×10⁹ N·m²/C²)·|–2.5×10^-9 C|·|+3.0×10^–9 C|/|1.8×10^–6 N|),

r = 0.1935415545 m,

or to two significant figures, 0.19 m.

(Response (A) is √(|q₁|·|q₂|/|F|); response (B) is (k·|q₁|·|q₂|/|F|); response (C) is √(k·(1×10^–18)·(|q₁| + |q₂|)/|F|).)

Section 30882
Exam code: quiz03C0u7
(A) : 0 students
(B) : 3 students
(C) : 2 students
(D) : 6 students

Success level: 54%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.67