Four charges are placed such that q1 = 1 nC, q2 = 2 nC, q3 = -6 nC, q4 = 2 nC with a specified arrangement. The bottom charge is q1. What is the magnitude and direction of the net force on q1?

• A. 1.14×10^-5 N, 0 degrees
• B. 1.14×10^-5 N, 45 degrees
• C. 1.14×10^-5 N, 90 degrees
• D. 2.28×10^-5 N, 90 degrees

Answer: (C)

Coulomb forces from multiple charges add as vectors, so the net force on q1 is the vector sum of the individual forces from q2, q3, and q4. Each force has magnitude k|q1 qi|/ri^2 and lies along the line joining q1 to qi. In this arrangement the horizontal components of those forces cancel each other out due to symmetry or equal opposing distances, leaving a net force that has only a vertical component. When you sum the vertical components, they point in the same direction and add to a magnitude of 1.14×10^-5 N. Since there is no horizontal component, the resultant is purely vertical, i.e., at 90 degrees to the horizontal.