How Do You Calculate the Initial Separation Between Two Charged Particles?

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To calculate the initial separation between two charged particles, the conservation of momentum and energy principles must be applied correctly. The equation used must differentiate between the velocities of the two particles, as they are not the same after release. The electrostatic force should be replaced with electrostatic potential energy in the energy conservation equation. The discussion emphasizes the importance of correctly identifying variables and understanding the physical principles involved in the problem. Properly applying these concepts will lead to the correct calculation of the initial separation.
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Homework Statement



One particle has a mass of 3.00 10-3 kg and a charge of +8.00 µC. A second particle has a mass of 6.00 10-3 kg and the same charge. The two particles are initially held in place and then released. The particles fly apart, and when the separation between them is 0.100 m, the speed of the 3.00 10-3 kg particle is 120 m/s. Find the initial separation between the particles.

Homework Equations



let the initial separation as r and final separation as d.
kq^2/r^2 = kq^2/d^2 + 1/2m1*V^2 + 1/2m2*V^2
is the the way to solve it? how can i determine the final velocity for the 6x10^-3 particle?

The Attempt at a Solution

 
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Are their any external forces acting on the system comprising the two charges ?
 
Nope.
 
What is conserved if there are no external forces acting on the system ?
 
momentum?
 
Yes . Use Conservation of Momentum.
 
udontai said:
let the initial separation as r and final separation as d.
kq^2/r^2 = kq^2/d^2 + 1/2m1*V^2 + 1/2m2*V^2
is the the way to solve it? how can i determine the final velocity for the 6x10^-3 particle?
The way you wrote the equation, you can solve it, but you'll get the wrong answer. Is the velocity for particle 1 the same as the velocity for particle 2? No. So why are you using the same variable, V, to represent those two quantities?

If you write the equation properly, you have one equations and two unknowns. You need a second equation if you hope to find specific values of each unknown.
 
(3.00 10-3 )x 0 + (6.00 10-3 ) x 0 = (3.00 10-3) x 120 - (6.00 10-3 ) x V
i this correct?
 
Tanya Sharma said:
Yes . Use Conservation of Momentum.

(3.00 10-3 )x 0 + (6.00 10-3 ) x 0 = (3.00 10-3) x 120 - (6.00 10-3 ) x V
i this correct?
 
  • #10
udontai said:
(3.00 10-3 )x 0 + (6.00 10-3 ) x 0 = (3.00 10-3) x 120 - (6.00 10-3 ) x V
i this correct?

Correct .

udontai said:
kq^2/r^2 = kq^2/d^2 + 1/2m1*V^2 + 1/2m2*V^2

There is another problem with this equation apart from what Vela has pointed .

What do these terms represent ?
 
  • #11
Tanya Sharma said:
Correct .



There is another problem with this equation apart from what Vela has pointed .

What do these terms represent ?

as i stated r = initial distance and d= final distance.
 
  • #12
udontai said:
as i stated r = initial distance and d= final distance.

Did I ask what r and d represent ?
 
  • #13
Tanya Sharma said:
Did I ask what r and d represent ?

i saw the r and d is highlighted from my computer screen so i thought you asked about it. lol my bad sorry
 
  • #14
But you still haven't answered my question in post#10 .
 
  • #15
Tanya Sharma said:
But you still haven't answered my question in post#10 .

so instead of kq^2/r^2 = kq^2/d^2 + 1/2m1*V^2 + 1/2m2*V^2.
it should be kq^2/r^2 = kq^2/d^2 + 1/2m1*(V1)^2 + 1/2m2*(V2)^2 as the velocity is different.
right?
 
  • #16
No . Sorry but you are not answering the question . I have explicitly remarked that there is another problem with the equation apart from what Vela has pointed .

Please explain what do terms I marked in red in post#10 represent ?
 
  • #17
kq^2/r2 represent the electrostatic force between the two charges
 
  • #18
udontai said:
kq^2/r2 represent the electrostatic force between the two charges

This is wrong .

How can you have force in conservation of energy equation ?

Instead of electrostatic force you need to have electrostatic potential energy of the two charges .
 
  • #19
Tanya Sharma said:
This is wrong .

How can you have force in conservation of energy equation ?

Instead of electrostatic force you need to have electrostatic potential energy of the two charges .

V = kq/r ?
 
  • #20
udontai said:
V = kq/r ?

No .

Please look up in your notes or book or on the web .
 
  • #21
E.P.E =qV
 
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