- #1
arl146
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Homework Statement
Find the charge Q that should be placed at the centre of the square of side 8.50E+0 cm, at the corners of which four identical charges +q = 3 C are placed so that the whole system is in equilibrium.
Homework Equations
F=(k*q1*q2) / r^2
The Attempt at a Solution
I know the solution is something like this:
Let r = side of square. That's 8.5 cm, right?
Without the center charge, F1 (on each charge, away from center) = kq^2/(sqrt(2)*r)^2 (diagonal charge) + 2*sqrt(0.5)*kq^2/r^2 (2 adjacent charges) =
k(q/r)^2*(0.5+sqrt(2)) = 2.1430705E13 N
F1 = -F (center charge Q to each corner charge q) = kqQ/(r*sqrt(0.5))^2 = 2kqQ/r^2
==> Q = -(F1)r^2/(2kq) = -(0.5+sqrt(2))q/2 = -2.87132 Cmy only question is this:
why does the F of the 2 adjacent charges = 2*sqrt(0.5)*kq^2/r^2
where does the 2*sqrt(1/2) come from? why isn't it just (2*k*q^2)/r^2