What is the explanation for the electrostatic force between two charged bodies?

[UchihaClan13]

Okay guys
It's no wonder I love electrostatics
I keep on getting so many doubts
Okay my doubt goes like this
Consider 2 charges(q₁and q₂ having masses m₁and m₂ (here i am assuming that these two aren't point charges and therefore don't have negligible volume/mass)
Okay so i am neglecting the gravitational force acting between them due to their masses
So the other attractive force(they are oppositely charged)acting on them is the electrostatic force of attraction
Which is equal in magnitude but opposite in direction for the two bodies
Now since they experience a net attractive force and have a certain mass(which i refer to as an intrinsic characteristic of a body which allows it to experience a force),they will also have a certain acceleration
Now if their initial separation is r
After a time dt,both of the charges move towards each other by say dr and dr₁ respectively
As a result the net force acting on them increases and therefore,assuming mass is constant,so does their net acceleration
So here,we have two bodies which experience distance variant forces and thus suffer varying accelerations
But there does arise some time when the separation between both the charges is a minimum
Could you guys tell me the steps required to find that using integration(I am not sure but i am guessing it's involved one way or another)
And is the analogy i implied in my question correct??
And what methods am i supposed to employ?
Some kind of the derivative of potential energy w.r.t to the separation distance becoming zero?
Some insight is much appreciated!:)
And if the answer involves too much integration,then could you guys just explain the scenario to me in mere,austere words??
Remain indebted to you all amazing people!:)

UchihaClan13

 

[Simon Bridge]

But there does arise some time when the separation between both the charges is a minimum..

... since the force is attractive, that happens when they touch each other.

More generally you have to solve the "central force problem" ... you can look it up.
But what you are considering is not electrostatics... electrodynamics is complicated. (i.e. accelerating charges radiate)

 

[UchihaClan13]

More generally you have to solve the "central force problem" ... you can look it up.
But what you are considering is not electrostatics... electrodynamics is complicated. (i.e. accelerating charges radiate)

Okay
But i still have a doubt
Charged particles which accelerate radiate energy as a consequence of Maxwell's Laws right
But can you apply maxwell's laws to quantum particles or particles of very small mass??
And sure i'll
Look up the "central force problem"UchihaClan13

 

[UchihaClan13]

And when the two particles touch each other,won't they have a certain normal force exerted on them due to each other?

 

[UchihaClan13]

thanks a lot,simonbridge for your suggestion
It really helped me!
:)
UchihaClan13

 

[UchihaClan13]

So you can reduce two bodies to one body of reduced mass μ=m₁m₂/m₁+m₂

And the difference between their positions can be treated as r
which will yield f=μ*r^..

 

[Drakkith]

Charged particles which accelerate radiate energy as a consequence of Maxwell's Laws right
But can you apply maxwell's laws to quantum particles or particles of very small mass??

In the 'classical limit', yes, Maxwell's laws apply just fine to even subatomic particles. They just aren't the full story when you want to explain certain phenomena such as the photoelectric effect or why electrons bound to nuclei don't radiate energy away and spiral down into the nucleus.

And when the two particles touch each other,won't they have a certain normal force exerted on them due to each other?

As long as your particles are bigger than the molecular or atomic realms, sure. Once you get down to particles at the atomic scale things start to behave a bit differently and you can't really use the concept of a normal force.

 

[Simon Bridge]

Okay ...
But can you apply maxwell's laws to quantum particles or particles of very small mass??

Its the other way around... maxwel is a subset of quantum mechanics.
You were asking questions in the realm of maxwel.

 

[UchihaClan13]

Okay so let me clear this up
An electron in a certain orbital has its energy quantized and does not fall into the nucleus as a consequence of the Heisenberg uncertainty principle

 

[UchihaClan13]

Or is it something else?

 

[Simon Bridge]

What are you trying to clear up?
Please make a clear problem statement.

 

[UchihaClan13]

What are you trying to clear up?
Please make a clear problem statement.

the reason why an electron bounded by a nucleus does not fall inside it
UchihaClan13

 

[Simon Bridge]

That is not a problem statement.

I am suddenly getting pedantic for two main reasons;
1. much of your "doubts" seem to stem from not being careful about how you talk about science, which is vague and suggestive when you need to be precise. (This is how the topic becomes a moving target for example.) I want to remove this possible source for confusion both to yourself and to people attempting to respond;
2. part of the purpose of these forums is to help enthusiastic inquirers like yourself to learn how to talk to scientists ... step 1 of the scientific method is to identify the problem. Until that is done, no progress can be made. This means you need to be able to write clear statements: your English is clearly up to the task. You are talking to scientists, you get the best from scientists when you can be precise.

So: what is it about "the reason why an electron [bound to] a nucleus does not fall inside it" that you have a problem with?

 

[UchihaClan13]

The problem that I possesses is the question itself
I mean,I require the answer of the particular question mentioned above i.e. i want to know the main reason as to why the phenomenon occurs
That's all
And thank you for pointing out my inaccuracies and mistakes
I am still a 9th grader
I will try my best to put problems into perspective so that all of you can get a clear picture of what i am trying to convey
UchihaClan13

 

[UchihaClan13]

I have my own explanation for it
Can you have a listen to it?(I am guessing it's wrong but still i want to ascertain)