# Time as a function of distance? electrostatic force

rebeka
time as a function of distance? electrostatic force

C = coulombs, Ke = electrostatic constant, d = distance, m = mass of electrons, v = velocity, c = a constant

F(d) = (KeC^2)/d

E(d) = (KeC^2) * integral (1/d) dd
= KeC^2(lnd2 - lnd1)

E = 1/2 mv^2
v = sqrt(2E/m)
= sqrt((2KeC^2(lnd2 - lnd1))/m)

d = vt
t = d/v

t(d) = (1/sqrt((KeC^2)/m)) * integral (1/sqrt(lnd - c)) dd
= ? what is that integral(antiderivative) does it even matter ?

rebeka
I know it only applies at our speeds so einsteins theory is irellevant to my question

Homework Helper
Gold Member
What is this about? What are you trying to find?

Is F(d) supposed to be a force? Because if so then your first equation is dimensionally incorrect.

rebeka
F(d) is force in Newtons between two static electric charges and so being what do you mean? dimensionally incorrect, that's the only thing I've been able to confirm (F(d) = (KeC^2)/d is a textbook equation)
I'm trying to find time passed as two charges(electrons) are moving away from each other ignoring all other rules of physics schroedingers equations too big and I want to make a fake it model

Last edited:
Staff Emeritus
rebeka said:
F(d) is force in Newtons between two static electric charges and so being what do you mean? dimensionally incorrect, that's the only thing I've been able to confirm (F(d) = (KeC^2)/d is a textbook equation)
I'm trying to find time passed as two charges(electrons) are moving away from each other ignoring all other rules of physics schroedingers equations too big and I want to make a fake it model

First of all, it is NEVER a good idea to simply spew a bunch of equations WITHOUT giving a general scenario of the problem AND explaining what you are trying to find. If you wish us to put some EFFORT into trying to help, you yourself should put at least the same amount of effort into giving an explanation as clear as possible. This will shorten the time and minimize a lot of grief in figuring out JUST what exactly is the problem.

Having said that, there's a lot of stuff that's very vague here.

1. You are trying to find "time passed as two charges are moving away from each other". You did not state if one charge is fixed in space or are both free to move. This can make a difference. If both are free to move, did you define where t=0 is? I.e. where did you choose the origin of the coordinate system? This system is where ALL your measurements of the location of the charges at any given time are referred to.

2. You used d = vt. This is not even close to being right. This is only valid IF v is a constant. Not only is v not a constant in this problem, the acceleration and force are also not a constant as a function of position! NOt only that, this "d" is undefined. Displacement or distance of what? This is connected to Point 1 in terms of the choice of origin/coordinate system.

There are other problems, but 1 and 2 are the major ones to start with.

Zz.

Homework Helper
Gold Member
Dearly Missed
Usually, it is rather unusual to determine "times" directly from energy arguments.

You should work directly with Newton's 2.law instead, unless I'm much mistaken.

rebeka
assume d1 has 0 velocity d1 can be any point it doesn't matter
it also doesn't matter if one is fixed or not Id love to hear the argument for that statement I was vague and the question would be extremely unusual to a college student(I didnt move this question to this section of the forum :) )however I assumed I was talking to highly knowledgeable people much more than myself these factors should already have been aware to the person(s) aiding in the problem I think this problem would be more readilly addressed by mathematicians or thermaldynamic phycisists I really don't even care about the physics :) I want to know the antiderivative of 1/sqrt of (lnx - constant)
I also appologize if I in anyway sound snarky but this problem has been plaguing me for some time

Staff Emeritus
rebeka said:
assume d1 has 0 velocity d1 can be any point it doesn't matter
it also doesn't matter if one is fixed or not Id love to hear the argument for that statement I was vague and the question would be extremely unusual to a college student(I didnt move this question to this section of the forum :) )however I assumed I was talking to highly knowledgeable people much more than myself these factors should already have been aware to the person(s) aiding in the problem I think this problem would be more readilly addressed by mathematicians or thermaldynamic phycisists I really don't even care about the physics :) I want to know the antiderivative of 1/sqrt of (lnx - constant)
I also appologize if I in anyway sound snarky but this problem has been plaguing me for some time

First of all, this is an E&M problem. So I don't know why you were looking for a "thermaldynamic physicists". ANY physicist has the knowledge of basic E&M.

Secondly, it DOES matter of one charge is fixed in terms of the DEGREE OF DIFFICULTY of the problem and how straightforward is the approach to the solution. If one charge can be fixed in space, then you can put your origin at THAT location, use that charge as the fields source, and the other moving charge as the "test" charge! Then the "r" that is in the field equation corresponds EXACTLY to the distance between the two sources.

On the other hand, if no charges is fixed, and you choose your origin as the midpoint in between the two charges (along a line), then r1 is the location of charge q1 and r2 is the location of charge q2, BOTH measured from the origin! Then the field equation would depend on the absolute sum of r1 and r2, and this is more condition has more in common with the image charge method than the first one.

So yes, it DOES make a boat-load of difference in terms of how difficult it can get by simply NOT specifying one way or the other.

Zz.

rebeka
being that I want the distance increase between the two particles and not the distance traveled by one or the other it doesn't matter and as for the thermaldynamics i was just spewing words such as yourself who has yet to shed any light on the problem

Homework Helper
I think the question is to find the relation between the time t and the distance r(t) between the electrons. Right?
For this we let the electrons are released from a distance r(0)
When the are at distance r(t) their speed can be calculated by conservation of energy(both will have same speed away from each other) as
mv^2 = KeC^2[ 1/r0 - 1/r ]

Now the force of interaction can be written as F(r) = KeC^2/r^2
[sorry, but I know this since last thirty years; there may be some misprint check it. If even then you find it correct then the force is not of the electrostatic interaction force between two charges, it will be some other force and the problem has nothing to do with physics it is some mathematical situation and solve accordingly]
and as we know that force F = mv(dv/dx) this with above equations may give the required differential equation. (Consider both the electrons are moving away from each other the velocity of separation is dr/dt = 2(dx/dt)
'I am not good in maths as well as in physics thus apologize in advance for the mistakes'

Staff Emeritus
rebeka said:
being that I want the distance increase between the two particles and not the distance traveled by one or the other it doesn't matter and as for the thermaldynamics i was just spewing words such as yourself who has yet to shed any light on the problem

Unlike you, I can't dive into something without understanding FIRST what the exact problem is. The understanding of the question is paramount BEFORE one tackles it. You expect someone to come in and solve an ambiguous problem? How would you know if someone has interpreted the question the SAME way that you interpret it? How would you know the solution offered is what you wanted the way you understood the problem?

Zz.

rebeka
t = (1/sqrt(KeC^2/m))* ((-e^lnd1(sqrt(pi))*(1 - Erf[sqrt(lnd1 - lnd2)])*(sqrt(-lnd1 + lnd2))/sqrt(lnd1 - lnd2)

well that's the equation according to calculus forums home use of mathematica which no one can readilly write the steps out to get there I have to learn more about calc. error functions(Erf, Erfi) before I can even manipulate that equation anyway occam seems fitting here and shroedingers wave equation almost seems just as simple so hey anyway thx

Last edited:
Dathascome
It has nothing to do with whether you are stupid or not, it has to do with the attitude you come here with when YOU are the one looking for help. There's something more respectable about a person who comes looking for help humbly.

Dathascome
No. Maybe you are thinking of K or Ke as you wrote initially as kinetic energy(which is in joules) but this K is the electrostatic constant and has nothing to do with kinetic energy or joules.

rebeka
Dathascome said:
No. Maybe you are thinking of K or Ke as you wrote initially as kinetic energy(which is in joules) but this K is the electrostatic constant and has nothing to do with kinetic energy or joules.

no I mean a spring rate constant is marked by K, actually both are not capitolized and that's all I mean by that wether it refers to joules is kind of the problem I am facing

Dathascome
I'm sorry I have no idea what this problem is. It seemed like an E&M problem but you're talking about spring constants and it does seem like you you are mixing up your K's. How about this, try starting from the beginning and stating your problem witout just putting formulas up and assuming people know what you mean. It will be easier to help like that.

rebeka
I think the first thing i should correct is E(r) = (KeC^2)/r

hence

v(r) = 2keC^2/mr

t(r) = m/(2KeC^2) (1/3(r2^3) - 1/3 (r1^3)

where
r is the distance between two freely moving charges
m is the total mass of the electrons
t is time
v is the rate of change of distance between both charges