Answer:
Ek = 8,79 [J]
Explanation:
We are going to solve this problem, using the energy conservation principle
State 1 or initial state (charges at rest t=0)
E₁ = Ek + U₁
As charge are at rest Ek = 0
And U₁ has two components
U₁₂ = K * Q₁*Q₂ / 0,4 and U₃₂ = K*Q₃*Q₂ / 0,6
U₁₂ = 9*10⁹* 60*10⁻⁶*10*10⁻⁶/0,4 ⇒ U₁₂ = 9*60*10*10⁻³/0,4
U₃₂ = - 9*10⁹* 20*10⁻⁶*10*10⁻⁶/0,6 ⇒ U₃₂ = - 9*20*10*10⁻³/0,6
U₁₂ = 540*10⁻2/0,4 [J] ⇒13,5 [J]
U₃₂ = - 180*10⁻² /0,6 [J] ⇒ - 3 [J]
Then E₁ = E₁₂ + E₃₂
E₁ = 10,5 [J]
At the moment of Q₂ passing x = 40 cm or 0,4 m
E₂ = Ek + U₂
We can calculate the components of U₂ in this new configuration
U₂ = U₁₂ + U₃₂
U₁₂ = 9*10⁹* 60*10⁻⁶*10*10⁻⁶/0,7 ⇒ U₁₂ = 9*60*10*10⁻³/0,7
U₁₂ = 540*10⁻²/0,7 U₁₂ = 7,71 [J]
U₃₂ = - 9*10⁹* 20*10⁻⁶*10*10⁻⁶/0,3 ⇒ U₃₂ = - 9*20*10*10⁻³/0,3
U₃₂ = - 9*20*10⁻²/0,3
U₃₂ = - 6
U₂ = 7,71 -6
U₂ = 1,71 [J]
Then as
E₂ = Ek + U₂ and E₂ = E₁
Then
Ek + U₂ = E₁
Ek = 10,5 - U₂
Ek = 10,5 - 1,71
Ek = 8,79 [J]
