A particle with charge 2-µC is placed at the origin, an identical particle, with the same charge,
is placed 2m from the origin on the x axis, and a third identical particle, with the same charge,
is placed 2m from the origin on the y axis. The magnitude of the force on the particle at the
origin is:
A. 9.0 × 10-3 N
B. 6.4 × 10-3 N
C. 1.3 × 10-2 N
D. 1.8 × 10-2 N
E. 3.6 × 10-2 N

1.3 × 10-2 N

Explanation:

Coulomb's law relate the force between two charges as

F = kq₁q₂ / d² where q₁ is at the origin

q₁ = q₂ = q₃= 2 µC = 2 × 10⁻⁶ C

F₁₂ = 8.99 × 10⁹ × 2 × 10⁻⁶ × 2 × 10⁻⁶ / 4 = 0.009 N along x axis

F₁₃ along y axis = 8.99 × 10⁹× 2 × 10⁻⁶ × 2 × 10⁻⁶ / 4 = 0.009 N along y axis

the magnitude of the force on the particle at the origin = √ (0.009² + 0.009²) = 1.27 × 10 ⁻² N approx 1.3 × 10-2 N

i believe the answer is a