Given three identical charges at separate positions how do you find the magnitude of the force on a small charge at the origin?

Question

There are identical Q = 4.40 x 10^-6 C charges located at three positions: (0,-1,2), (1,2,0), and (-2,0,-1). Coordinates are listed in units of meters. What is the magnitude of the force that a charge of -1 x 10^-6 C feels at the origin?

So I found the right equation by kind of reverse engineering the answer but I don t understand it. Any help would be welcome!

Answer 1

You may have to go through a series of tedious calculations.  Find the x, y, and z components of the 3 forces when you pair the charge at (0,0,0) with each of the three Q charges.  You can calculate the magnitude of the force for each pair using Coulombs law, and then use trigonometry to project that magnitude along the x, y, and z axes to get the 3 components.  Be careful with the signs of the components, because Q is positive and the charge at the origin is negative, so the force must point from the origin toward the position of Q.  Do this for all three pairs.  Then get the net x component by adding the x components of the three pairs, and similarly get the net y and z components.  The magnitude of the net force will be the square root of the sum of the squares of the three net components.