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