Question

Four identical point charges of q = 4.64 nC are at the four corners of a square with a side length of 13.5 cm as shown in the figure. What charge Q should be placed at the center of the square to keep the other four charges in equilibrum?

Answer 1

Figure the force on one of the corners (the sum of the forces from the three other corners). Then figure Q such that it balances this force.

Force on one corner:

kQq(1/s^2 *.707 + 1/s^2 (.707)+ 1/*sqrt2*s)^2)
= kqq/s^2*(1.414+.5) check that I did it in my head.

that is the force on each corner.

Now, balance that with Q at distance s*.707

forcebalance=kqQ(1/.5s^2)=2kqQ/s^2

solve for Q. Check my work.

Answer 2

so would it be

(2)(9.0e9)(4.64)(Q)/0.707^2