Two particles, with charges of q_1 - 60.0 nC and q_2 = -60.0 nC are placed at th

Question

Two particles, with charges of q_1 - 60.0 nC and q_2 = -60.0 nC are placed at the points with coordinates (0, 4.00 cm) and (0, -4.00 cm) as shown in the figure below. A particle with charge q_3 = 30.0 nC is C, located at the origin. Find the electric potential energy of the configuration of the three fixed charges, A fourth particle, with a mass of 2.04 times 10^-13 kg and a charge of q_4 = 120.0 nC is released from rest at the point (3.00 cm, 0), Find its speed after it has moved freely to a very large distance away. m/s

Explanation / Answer

(a)

PE of configuretion,

U = k*(q1*q2 / r1 + q2*q3 / r2 + q1*q3 / r3)

U = 9*10^9*10^(-9)*(-60*60 / 0.08 - 60*30 / 0.04 + 60*30 / 0.04)

U = 40.5*10^4 J

(b)

PE of q4 due three other charges,

U' = k*q4*(q1 / r1 + q2 / r2 + q3 / r3)

U' = 9*10^9*120*10^(-9) * (60 / 0.05 + 60 / 0.05 - 30 / 0.03)

U' = 15.12*10^5 J

at a very large distance,

U = 0

apply law of energy conservation,

KEi + Ui = KEf + Uf

0 + 15.12*10^5 = (1/2)*m*v^2 + 0

v^2 = 2*15.12*10^5 / 2.04*10^(-13)

v = 3.85*10^9 m/s

answer

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