Question 24.103: In Fig. 24-72, two particles of charges q1 and q2 are fixed ......

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

In Fig. 24-72, two particles of charges q $_1$ and q $_2$ are fixed to an x axis. If a third particle, of charge +6.0 μC, is brought from an infinite distance to point P, the three-particle system has the same electric potential energy as the original two-particle system. What is the charge ratio $q_1/q_2$ ?

1360823-Figure 24.72

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Since the electric potential energy is not changed by the introduction of the third particle, we conclude that the net electric potential evaluated at P caused by the original two particles must be zero:

$\frac{q_1}{4 \pi \varepsilon_0 r_1}+\frac{q_2}{4 \pi \varepsilon_0 r_2}=0 .$

Setting r $_1$ = 5d/2 and r $_2$ = 3d /2 we obtain $q_1=-5 q_2 / 3,\,\, \text { or } q_1 / q_2=-5 / 3 \approx-1.7$ .

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