Physics quiz question: total electric field direction between two charges

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

Two point charges are held at fixed positions. A +4.0 µC charge is at x = –1.0 cm, and a +8.0 µC charge is at x = +2.0 cm. The electric field at x = 0 is directed to the:
(A) left.
(B) right.
(C) (There is no direction, as the electric field would be zero.)
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (B)

The electric field vector at x = 0 due to the +4.0 µC source charge points to the right, out away from this positive source charge. The magnitude of the electric field at x = 0 due to the +4.0 µC source charge is:

E₄ = k·|Q|/r²,

E₄ = k·|+4.0 µC|/(1.0 cm)²,

E₄ = (4.0 µC/cm²)·k.

The electric field vector at x = 0 due to the +8.0 µC source charge points to the left, out away from this positive source charge. The magnitude of the electric field at x = 0 due to the +8.0 µC source charge is:

E₈ = k·|Q|/r²,

E₈ = k·|+8.0 µC|/(2.0 cm)²,

E₈ = (2.0 µC/cm²)·k.

The total electric field at x = 0 due to both source charges is the vector addition of the individual electric field vectors at that location. Since the electric fields due to the +4.0 µC source charge and the +8.0 µC source charge point in opposite directions at x = 0, the direction of the total electric field there would point to the right (as the magnitude of E₄, which points to the right is greater than the magnitude of E₈, which points to the left).

(As an aside, the magnitude of the total electric field at x = 0 would be the difference of the two individual electric field magnitudes, as the electric fields due to the +4.0 µC source charge and the +8.0 µC source charge point in opposite directions:

E = |E₈| – |E₄|,

E = (4.0 µC/cm²)·k – (2.0 µC/cm²)·k,

E = (2.0 µC/cm²)·k,

E = (2.0 µC/cm²)((1 C)/(10⁶ µC))·((100 cm)/(1 m))²·(8.99×10⁹ N·m²/C²),

E = 179,800,000 N/C,

or to two significant figures, the magnitude of the total electrical field at x = 0 is 1.8×10⁸ N/C.)

Sections 30882, 30883
Exam code: quiz03d3St
(A) : 10 students
(B) : 13 students
(C) : 5 students
(D) : 0 students

Success level: 46%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.40