Coulomb's law:

$\overline{){\mathbf{F}}{\mathbf{=}}\frac{\mathbf{k}{\mathbf{q}}_{\mathbf{1}}{\mathbf{q}}_{\mathbf{2}}}{{\mathbf{r}}^{\mathbf{2}}}}$

diagonal squared = 2L^{2}

F_{12} = kq^{2}/L^{2}

F_{23} = kq^{2}/L^{2}

F_{24} = kq^{2}/(2L^{2})

$\begin{array}{rcl}{\mathbf{r}}_{\mathbf{25}}& \mathbf{=}& \frac{\sqrt{\mathbf{2}}\mathbf{\xb7}\mathbf{L}}{\mathbf{2}}\\ {\mathbf{\left(}{\mathbf{r}}_{\mathbf{25}}\mathbf{\right)}}^{\mathbf{2}}& \mathbf{=}& \frac{\mathbf{2}{\mathbf{L}}^{\mathbf{2}}}{\mathbf{4}}\\ & \mathbf{=}& \frac{{\mathbf{L}}^{\mathbf{2}}}{\mathbf{2}}\end{array}$

Four equal positive point charges, each of charge 5.7 µC , are at the corners of a square of side 9.2 cm.

What charge should be placed at the center of the square so that all charges are at equilibrium?

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