question below please answer asap

Question

Consider four point charges arranged in a
square with sides of length L. Three of the
point charges have charge q and one of them
has charge −q. What is the magnitude of
the electric force on the −q charge due to the
three q charges?

 

I understand this is an addition of vectors but im confused about how to find the resultant vector.

Answer 1

I will set this up for you and get you to the point where you can just plug in numbers, and you take it from there.  Assume -q is at the origin, and the three +q's are at (L,0), (L,L), and (0,L).  Use Coulomb's law to get separately the x and y components of the force, and then combine the components into a vector.

 

Add the forces in the order in which I listed the coordinates of the three +q's.  Note that the only + charges that contribute to F_x are the charges at (L,0) and (L,L).

 

F_x = -kq² [1/L² + cos45°/(2L²)] 

 

Note that the only + charges that contribute to F_y are the charges at (0,L) and (L,L).

 

F_y = -kq² [1/L² + sin45°/(2L²)]

 

The resultant force vector is

 

F = F_xi + F_yj

 

You can finish from here.