Physics quiz question: electric force on test charge

Physics 205B Quiz 3, spring semester 2017
Cuesta College, San Luis Obispo, CA

Two point charges are held at fixed positions. A –2.5 nC charge is at x = 0 and a +3.0 nC charge is at x = +3.0 cm. The electric force on the +3.0 nC charge at x = +3.0 cm is directed to the __________ and its magnitude is __________.
(A) left; 2.2×10^–6 N.
(B) left; 7.5×10^–5 N.
(C) left; 2.5×10⁴ N.
(D) right; 2.2×10^–6 N.
(E) right; 7.5×10^–5 N.
(F) right; 2.5×10⁴ N.

Correct answer (highlight to unhide): (B)

The force on the +3.0 nC charge at x = +3.0 cm points to the left, as it is being attracted by the –2.5 nC charge at the origin.

The magnitude of the force on the +3.0 nC charge at x = +3.0 cm is given by:

|F| = k·|q₁|·|q₂|/(r²),

where q₁ = 2.5 nC is the source charge at the origin, and q₂ = +3.0 nC is the test charge (the charge that force is being exerted on) at x = +3.0 cm, and the proportionality constant k = 8.99×10⁹ N·m²/C². Then:

|F| = (8.99×10⁹ N·m²/C²)·|–2.5×10^–9 C|·|+3.0×10^–9 C|/(3.0×10^–2 m)²,

|F| = 0.00007491666667 N,

or to two significant figures, the magnitude of the force on the +3.0 nC charge is 7.5×10^–5 N.

(Response (A) has a magnitude of k·|q₁|·|q₂|/r; response (C) has a magnitude of k·|q₁|/(r²). Responses (D)-(F) have the wrong force direction.)

Sections 30882, 30883
Exam code: quiz03d3St
(A) : 2 students
(B) : 18 students
(C) : 2 students
(D) : 0 students
(E) : 4 students
(F) : 2 students

Success level: 64%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.40