Calculating Velocity in a Charge/Field Interaction: A Homework Challenge

In summary, the conversation revolved around solving for the speed/velocity of ships using superposition and conservation laws. The potential energy between the ships was discussed, with the total potential energy being 3* kq^2/D. As the ships tend towards infinite separation, the potential energy will turn into kinetic energy, which can be solved for using the equation 3* kq^2/D=1/2Mv^2. The justification for the multiplication by 3 was also discussed.
  • #1
Callix
106
0

Homework Statement


PHYSICS.png


Homework Equations


F=kqQ/D^2=Ma
E=kQ/D^2
D=vt?

The Attempt at a Solution


So far, I've been able to label the forces on each ship through superposition. But that is all I currently able to understand. I know that my end solution is a speed/velocity, but I am not sure how to get there with the given (Q, t, D, and M)

Any help and direction would be greatly appreciated!
 
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  • #2
Have you considered a conservation law approach?
 
  • #3
I have not because we haven't discussed it. How might I use said approach?
 
  • #4
Callix said:
I have not because we haven't discussed it. How might I use said approach?
Usually one considers the trade off between potential and kinetic energy. What form of potential energy is involved here?
 
  • #5
gneill said:
Usually one considers the trade off between potential and kinetic energy. What form of potential energy is involved here?

There is definitely potential energy between each ship.
 
  • #6
Callix said:
There is definitely potential energy between each ship.
Yes... what type and how much?
 
  • #7
gneill said:
Yes... what type and how much?

Electrical Potential Energy
U12=kq1q2/D
U23=kq2q3/D
U13=kq1q3/D
 
  • #8
What's the total PE of the system in terms of the variables that you were given?
 
  • #9
U(total) = 3* kq^2/D, right?
 
  • #10
Callix said:
U(total) = 3* kq^2/D, right?
Looks good.

So how will that change as the ships all tend towards infinite separation? Where will it go?
 
  • #11
gneill said:
Looks good.

So how will that change as the ships all tend towards infinite separation? Where will it go?

All the potential will simply turn into kinetic energy right?
 
  • #12
Callix said:
All the potential will simply turn into kinetic energy right?
That's right.
 
  • #13
gneill said:
That's right.

Alright, so then 3* kq^2/D=1/2Mv^2 and just solve for v
 
  • #14
Callix said:
Alright, so then 3* kq^2/D=1/2Mv^2 and just solve for v
Remember that the energy will be split three ways.
 
  • #15
gneill said:
Remember that the energy will be split three ways.

So is the multiplying by 3 completely necessary if the charges and D are the same? Couldn't I just solve it as kq^2/D=1/2Mv^2
 
  • #16
Callix said:
So is the multiplying by 3 completely necessary if the charges and D are the same? Couldn't I just solve it as kq^2/D=1/2Mv^2
Sure. In your presented solution be sure to state why you are justified in doing it.
 
  • #17
gneill said:
Sure. In your presented solution be sure to state why you are justified in doing it.

Ah okay, I understand now! Thank you very much! :)
 

FAQ: Calculating Velocity in a Charge/Field Interaction: A Homework Challenge

What is the "Charge/Field/Velocity Problem" in science?

The "Charge/Field/Velocity Problem" is a concept in electromagnetism that deals with the relationship between electric charges, electric fields, and the velocity of a charged particle. It is also known as the "Lorentz force law" or "Lorentz equation".

How does the "Charge/Field/Velocity Problem" affect the movement of charged particles?

The "Charge/Field/Velocity Problem" explains how an electric field can exert a force on a charged particle, causing it to accelerate or change direction. This is known as the Lorentz force, and it is an essential concept in understanding the behavior of electrically charged objects in the presence of an electric field.

Can the "Charge/Field/Velocity Problem" be applied to all types of charged particles?

Yes, the "Charge/Field/Velocity Problem" applies to all types of charged particles, including electrons, protons, and ions. It also applies to both stationary and moving charged particles.

How is the "Charge/Field/Velocity Problem" used in practical applications?

The "Charge/Field/Velocity Problem" is used in many practical applications, such as in the design of electric motors and generators, particle accelerators, and in the study of plasma physics. It is also crucial in understanding the behavior of charged particles in space, such as in the Earth's magnetosphere.

Are there any limitations to the "Charge/Field/Velocity Problem"?

While the "Charge/Field/Velocity Problem" is a fundamental principle in electromagnetism, it is not a complete description of all electromagnetic phenomena. It does not take into account quantum effects and relativistic effects, which are necessary to describe the behavior of charged particles at the atomic and subatomic levels. However, it is still a powerful tool for understanding and predicting the behavior of charged particles in many practical situations.

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