What is the Minimum Distance Between Moving Identical Particles in Vacuum?

[Kostas Tzim]

Homework Statement

Two identical particles with $$ m=4,5 mg $$ and $$ q= 30 nC $$ are moving in vacuum in same direction. the paricles facing each other the time of the movement O --> <-- O like this.The time their distance is $$25cm$$

Homework Equations

Which will be the minimum distance between them?
$$ ε0=8,85 10^{-12}C ^2 /Nm^2 $$ , Ignore the gravitational forces

The Attempt at a Solution

Its a problem from the national competition. I would appreciate some help, i thought about using the conservation of energy

 

[gneill]

Its a problem from the national competition. I would appreciate some help, i thought about using the conservation of energy

Can you show us your attempt using conservation of energy? You might also need another conservation law.

We can't provide additional help until we see your effort.

 

[haruspex]

i thought about using the conservation of energy

Conservation of energy would be the way to go. Can you put a bit more detail around that?

 

[Kostas Tzim]

Since we ignore the gravitational field we get (i really don't know the english physics terminology) $$ E_(start)=E_(end) $$ $$ <=> $$ $$ k_c\dfrac{q*q}{r} + 2\dfrac{1}{2}mv^2= ?$$ this is my thought, since we have two particles this is why i put the $$ 2 $$ in front of the starting Kinetic Energy moreover the electrical dynamical energy is given by the above equation. i don't know what to do next, i suppose in the second part of the equation i have to appear the $$ r_min $$ also i don't know what the $$ε_0$$ is given for. This problem is back from 2009 ,maybe the school curriculum had changed back then, you know in greece sadly we have not a standard curriculum the books are changing without a real reason, think that I am nearly 17 years old and i have no clue about the magnetic field all the previous years this topic was In the curricula and for some reason this year it got out, now i have to study it bymyself since i think its really important

 

[gneill]

Were you given values for the initial speeds of the particles, or are you to find a symbolic result?

What quantities will have to go on the right hand side of your equation (where your ? is)?
What can you say about the relative speeds of the particles when they are at minimum distance?

 

[Kostas Tzim]

Oh nooo,forgive me $$ 4 m/s $$ by the time their distance is $$ 25 $$ cm

 

[Kostas Tzim]

First of all on the right side i would have the kinetic energy and the potential energy...one of them will be $$0$$ i think it'll be kinetic but i can't prove it...i didnt understand the concept of the problem well, i hope you can understand my translation

 

[gneill]

You should be able to argue that at minimum distance the two particles must stop approaching each other (otherwise they would get closer still). Then the only thing they can do is start to separate again. At the instant of closest approach then, what is their relative speed?

Assume this closest distance is r. What is the electric potential energy at that point?

By the way, if you use "##" rather than "$$" as Latex tags the code will stay embedded in the current text line.

 

[Kostas Tzim]

Thanks for the tip, then its kind of easy the right side gives us the $k_c\dfrac{q^2}{r_{minimum} }$ i suppose, As you mentioned when the particles reach the $minimum$ distance then they start separated is this separation violent? or they separate with the initial speeds...theoretically can't they collide? I understand that they distance cannot be equal to $0$ since we agree that even particles have dimensions. Enough of the theoretical talking, i still don't know how to use the $\epsilon_0$

btw: the preview option crushes...it appers a black hole :P and Thanks for your time..im sorry if I am being annoying with silly questions

 

[gneill]

Thanks for the tip, then its kind of easy the right side gives us the $k_c\dfrac{q^2}{r_{minimum} }$ i suppose, As you mentioned when the particles reach the $minimum$ distance then they start separated is this separation violent? or they separate with the initial speeds...theoretically can't they collide? I understand that they distance cannot be equal to $0$ since we agree that even particles have dimensions. Enough of the theoretical talking, i still don't know how to use the $\epsilon_0$

The separation and approach will look like mirror images (time-wise). No violent changes -- that would involve some sudden energy change that has no source in this system. Since the electrical force grows without bound as the distance approaches zero, the particles cannot touch even if they were theoretical point-particles.

The constant $k_c$ is actually "made from" $\epsilon_o$: $~~~~~k_c = \frac{1}{4 \pi \epsilon_o}$

btw: the preview option crushes...it appers a black hole :P and Thanks for your time..im sorry if I am being annoying with silly questions

That might be a problem peculiar to your machine. What browser and Operating System are you running?

 

[Kostas Tzim]

Oh god yeah,! totally forgot it..now its clear..all these problems I am solving are sooo tricky, i mean I am trying hard, complicated thoughts cyrcling my mind and when i fail to solve it and look up to the solution its simple it only needs an observation..maybe these days ill upload more problems..i think they are useful for other students that are here too. Anyway, thanks a lot for the help I am using chrome, windows7 64

 

[gneill]

chrome, windows7 64

What exactly happens when you select Preview? Does anything appear?

 

[Kostas Tzim]

.

 

[Kostas Tzim]

http://prntscr.com/6az9xi this...

 

[gneill]

That's odd. You might want to try clearing your browser's cache and history. I haven't heard of any other reports of this symptom occurring with Chrome or other browsers. If you have another browser on your machine you might want to give it a test.

 

[Kostas Tzim]

actually my clock has stopped that;s cause of the battery i think its over. i have to get another battery..maybe this causes the problem

 

[gneill]

actually my clock has stopped that;s cause of the battery i think its over. i have to get another battery..maybe this causes the problem

Possibly. Certain cache entries or routes may no be getting flushed or updated on time.

 

[Kostas Tzim]

is it bad for the PC that the battery stays inside?...i haven't bought a new one yet

 

[gneill]

is it bad for the PC that the battery stays inside?...i haven't bought a new one yet

It's hard to say without knowing what kind of battery and how old it might be.

 

[Kostas Tzim]

well i built this pc 1 year ago same month, the battery is button type CR2032 3V

 

[gneill]

well i built this pc 1 year ago same month, the battery is button type CR2032 3V

There shouldn't be any problem with that type of battery for several years, if it's physical integrity you're worried about.

 

[Kostas Tzim]

i read that several people have this problem with the same motherboard (Asus Maximus VI hero)..i don't know maybe the batteries from the time were placed were problematic