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

Fundamentals of Physics Extended – Instructor’s Solutions Manual [1360823]

In Fig. 21-25, four particles form a square. The charges are $q_1=+Q, q_2 = q_3 = q$ , and q $_4$ =-2.00 Q. What is q/Q if the net electrostatic force on particle 1 is zero?

1360823-Figure 21.25

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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 $q / Q=1 / \sqrt{2}=0.707$ .

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