Chap_20_Disc[1]

# Chap_20_Disc[1] - 20-39(a Find the electric potential at...

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20-39 . •• (a) Find the electric potential at point P in Figure 20–26. (b) Suppose the three charges shown in Figure 20–26 are held in place. A fourth charge, with a charge of +6.11 C and a mass of 4.71 g, is released from rest at point P. What is the speed of the fourth charge when it has moved infinitely far away from the other three charges? Picture the Problem : The configuration of the three point charges is shown at the right. Strategy: Find the electric potential at point P by summing the potentials due to the three charges at the vertices of the triangle. Then multiply the potential by the charge to determine its electric potential energy. Set the potential energy equal to the kinetic energy to find the speed of the charge when it is infinitely far away from the other three charges. The distance between the point P and the second charge, at the top of the triangle, is 4 q 2 r 2 2 1 2 2 1.25 m 1.25 m 1.08 m. r Solution: 1. (a) Sum the potentials from each of the three charges: 2 2 3 3 1 2 1 2 1 2 3 1 2 3 6 6 6 9 N m C 1 1 2 2 2.75 10 C 7.45 10 C 1.72 10 C 8.99 10 76.7 kV 1.25 m 1.08 m 1.25 m kq q kq kq q q V k r r r r r r 2. (b) Set and solve for v : i i f U K U K f 2 1 4 2 6 4 0 0 2 6.11 10 C 2 76,700 V 14.1 m/s 0.00471 kg q V mv q v V m

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