Two more +Q charges are held in place the same distance "s" away from the +q charge as shown. Consider the following student dialogue concerning the net force on the +q charge:
The two added charges are written with blue Q's
Student 1: "The net electric force on the +q charge is now three times as large as before, since there are now three positive charges exerting forces on it."
Student 2: "I don't think so. The force from the +Q charge on the left will cencel the force from +Q charge on the right. The net electric force will be the same as in part A."
The Attempt at a Solution
What I did was I drew out that diagram above on a piece of paper and each line I drew pointing from the +q to the Q was exactly the same length. Next, I drew the force vectors after(in this case, it would be repulsion), and they ended up looking something like this:
I found that it was less than three times one of the forces. Also, they could'nt have cancelled each other out because they were repulsive. However, I know I could show this through visually, but how could I prove it mathematically (using physics formulae) that this is correct?