Five equal charged particles +q are placed on a square as illustrated. A sixth charged particle +q' is placed at the center O. What is the direction of the vector sum of the forces exerted on q'?
The forces exerted by the charged particles at B and C are equal in magnitude and opposite in direction so they add up to zero. The force exerted by the particle at A on q' points along OD. The force exerted by the particle on the right side of the square points to the left, and that by the particle at the bottom points up. These last two forces are twice as large as that from the particle at A (because they are closer by a factor sqrt(2)) and they add up to a force that points along OA. Their vector sum is larger than each force individually, which in turn is larger than the force due to the particle at A. Consequently the vector sum of all the forces points along OA.