Four charged particles are at rest at the corners of a square (Fig. P26.14). The
ID: 1427503 • Letter: F
Question
Four charged particles are at rest at the corners of a square (Fig. P26.14). The net charges are q 1 5 q 2 5 2 2.65 m C and q 3 5 q 4 5 2 5.15 m C. The distance between particle 1 and particle 3 is r 13 5 1.75 cm. a. N What is the electric potential energy of the four-particle system? b. C If the particles are released from rest, what will happen to the system? In particular, what will happen to the system’s kinetic energy as their separations become infinite?
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Explanation / Answer
q1=q2 =2.65 uC, , q3 =q4 = -5.15 uC
r24 = r13 = 1.75 cm
r34 =r41=r12 =r23 = 1.75/2^1/2 = 1.24 cm
electirc potential energy U = kq1q2/r
k =9*10^9 N.m^2/C^2
Total potential energy U = U12+U23+U34+U41+U24+U13
U = (9*10^9*2.65*2.65*10^-12/0.0124)+ (9*10^9*5.15*5.15*10^-12/0.0124) -(2*9*10^9*5.15*2.65*10^-12/0.0124) - (2*9*10^9*5.15*2.65*10^-12/0.0175)
U = -9.5 J
(b) System potential energy is negative. If charges are relased from rest , the distance between them is increased.
If the distance between them is infinity then potential energy will be zero .So kinetic energy becomes maximum