Two particles, with charges of q_1 = 10.0 nC and q_2 = -10.0 nC, are placed at t

Question

Two particles, with charges of q_1 = 10.0 nC and q_2 = -10.0 nC, are placed at the points with coordinates (0, 8.00 cm) and (0, -8.00 cm) as shown in the figure below. A particle with charge q_3 = 5.0 nC is located at the origin. (a) Find the electric potential energy of the configuration of the three fixed charges. J (b) A fourth particle, with a mass of 1.74 times 10^-13 kg and a charge of q_4 = 20.0 nC, is released from rest at the point (6.00 cm, 0). Find its speed after it has moved freely to a very large distance away. m/s

Explanation / Answer

(A) Potential energy of two point charge system is given as

PE = k q q' / d

k = 9 x 10^9, q1 = 10 x 10^-9 C, q2 = -10 x 10^-9 C

q3 = 5 x 10^-9 C

PE = [ k q1 q3 / 0.08] + [ k q2 q3 / 0.08] + [ k q1 q2 / 0.16]

PE = -5.625 x 10^-6 J ........Ans

(B) POtential at the location of q4:

V1 = [ k q1 / sqrt(0.08^2 + 0.06^2)] + [ k q3 / 0.06] + [ k q2 /sqrt(0.08^2 + 0.06^2) ]

V1 = 750 Volt

potential at very large distance away, V2 = 0

change in KE = - q deltaV

1.74 x 10^-13 v^2 /2 = (20 x 10^-9) (0 - 750)

v = 1.31 x 10^4 m/s

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