Where does the 6 come from in F24 calculation

[Gemy4]

Hi first post sorry if I didn't follow anyone specific rule. Me and my fiancee are stumped how my physics 2b teacher got 6kq^2/L^2 for F24. We understand that where r= L square root2/2 is squared so the result is L^2. But where in the heck did the 6 come from in 6kq^2.

 

[ehild]

$$(L\frac{\sqrt{2}}{2})^2=\frac{2L^2}{4}=L^2/2$$

ehild

 

[inutard]

Yes. As ehild said in his post, the result of r^2 is (L^2)/2. So the 2 multiplies into the 3 on 3q and it becomes 6q^2 (pardon me for my lack of Tex).

 

[Gemy4]

Beautiful! Also why is it that she used q1 and q4 vs. q3 and q4. I realize it will produce the same answer.

 

[inutard]

Your teacher indicated q1-q4 and q3-q4 because they are two forces of the same magnitude/size pulling in opposite directions. Because these two forces are pulling in opposite directions, their net force cancel to 0.
However, your teacher also killed two birds with one stone because her equations following F14 = F34 not only indicated that the two forces canceled out, it also calculated F24 (as each of the three charges, q1,q2,q3 , provide the same force in different directions). Since F24 does not have any other force cancelling it out, it provides the only force that moves the q4 charge. And that force is 6kq^2/L^2, as you've indicated in your first post.