Four equal point charges of $+4.0\ \text{nC}$ each are fixed at the corners of a square of side $10\ \text{cm}$, as in the figure. A fifth point charge $Q$ is then fixed at the centre of the square. It is chosen so that the total electrostatic potential energy of all five charges is zero. In other words, no net work is needed to bring all five charges in from very far apart, one by one, to these places. What is $Q$, with its sign? Give the answer in $\text{nC}$, to two decimal places.

Fig. 1: A square of side 10 cm with a point charge of plus 4.0 nanocoulombs at each of its four corners and a charge Q, of unknown size and sign, at its centre.