Two charged particles are placed on x-axis. The first charged particle has a mas

Question

Two charged particles are placed on x-axis. The first charged particle has a mass of 1.5*10^-5 kg and a charge of Q1= 2*10^-6 C, and remains at the origin. A second charged particle has a mass of 4*10^-5 kg and a charge of (Negative, Q2= -8*10^-6 C), and is released from rest at x=60 cm.

a) What is the speed of the second particle when it moves 45cm?

b) Does the potential energy of the system increase or decrease?

c) does the second charged particle move with constant acceleration?

Answer: (a) 1.9*10^2 m/s, (b) decrease (c) No, because the electric force between two charges is not constant ( F=kQ1Q2/r^2, r is kept changing.)

Can you please provide the all steps and explanation of how to get these answers?

Explanation / Answer

initial potential energy of the system of two charges

Ui = k*Q1*Q2/r1

initial kinetic energy of the system = 0

total inital energy of the system = Ei = k*Q1*Q2/r1

the charge Q2 has moved 45 cm towards Q1

the charge Q2 is at r2 = 15 cm = 0.15 m

Uf = k*Q1*Q2/r2

KEf = 0.5*m2*v^2

Ef = k*Q1*Q2/r2 + 0.5*m2*v^2

Ef = Ei

k*Q1*Q2/r2 + 0.5*m2*v^2 = k*Q1*Q2/r1

-(9*10^9*2*10^-6*8*10^-6)/0.15 + 0.5*4*10^-5*v^2 = -(9*10^9*2*10^-6*8*10^-6)/0.6

v = 1.9*10^2 m/s

++++++++++++++

(b)

Ui = -0.24 J

Uf = -0.96 J

Uf < Ui

the final potential energy decreases

++++++++++++

c) NO

the force acting on the Q2 = F = k*Q1*Q2/r^2

here as Q2 moves towards Q1 the distance between Q1 & Q2 decreases and the force changes

acceleration = F/m2

as the force is not constant acceleration is not constant

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