6. 12 points SerPOP4 20.P.018. My Notes Ask Your Teacher Two particles, with cha

Question

6. 12 points SerPOP4 20.P.018. My Notes Ask Your Teacher Two particles, with charges of 90.0 nC and -90.0 nC, are placed at the points with coordinates (0, 12.00) cm and (0, -12.00) cm as shown in Figure P20.18. A particle with charge 45.0 nC is located at the origin. Figure P20.18 (a) Find the electric potential energy of the configuration of the three fixed charges. (b) A fourth particle, with a mass of 2.07 x 10-13 kg and a charge of 180.0 nC, is released from rest at the point (9.00, 0) cm. Find its speed after it has moved freely to a very large distance away. m/s Submit Answer Save Progress Practice Another Version

Explanation / Answer

let q1 = 90 nc
q2 = -90 nc
d = 12 cm = 0.12 m
q3 = 45 nc

a)

U = U12 + U23 + U31

= k*q1*q2/r12 + k*q2*q3/r23 + k*q3*q1/r31

= k*q1*q2/r12 (since q2 = -q1)

= 9*10^9*90*10^-9*(-90*10^-9)/(2*0.12)

= -3.04*10^-4 J

b) Potential at the fourth point charge,

V = V1 + V2 + V3

= k*q1/r1 + k*q2/r2 + k*q3/r3

= k*q3/r3 (since q2 = -q1)

= 9*10^9*45*10^-9/0.09

= 4500 V

potential at infinite distance, vf = 0

workdone on the fourst charged particle, W = q*delta_V

(1/2)*m*v^2 = q4*(Vf - Vi)

v = sqrt(2*q4*(Vf - Vi)/m)

= sqrt(2*180*10^-9*(4500 - 0)/(2.07*10^-13))

= 8.85*10^4 m/s

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