Question 21.70: In Fig. 21-25, four particles form a square. The charges are......

For the net force on q_1 = +Q to vanish, the x force component due to q_2 = q must exactly cancel the force of attraction caused by q_4 = –2Q. Consequently,

\frac{Q q}{4 \pi \varepsilon_0 a^2}=\frac{Q|2 Q|}{4 \pi \varepsilon_0(\sqrt{2} a)^2} \cos 45^{\circ}=\frac{Q^2}{4 \pi \varepsilon_0 \sqrt{2} a^2}

or q=Q / \sqrt{2} . This implies that q / Q=1 / \sqrt{2}=0.707 .