How the distance from centre decides type of charge motion?

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The discussion centers on how the distance from the center of a charge distribution affects the type of motion exhibited by a test charge. A charge far from the center experiences oscillatory motion due to an inverse square force law, while a charge close to the center undergoes simple harmonic motion (SHM) because the force becomes directly proportional to the distance from the origin. The spherical shell theorem is referenced to explain that only the charge within a certain radius contributes to the net electric field experienced by the test charge. The conversation also clarifies that the acceleration in SHM is proportional to displacement, distinguishing it from general oscillatory motion. Ultimately, the relationship between force and distance is crucial in determining the type of motion.
  • #31
gracy said:
8 times?
Correct.

Now, with eight times the charge you have an electric field that is eight times as strong. But remember that we doubled the radius of the shell. If the test charge is on the surface of this shell, it is now twice as far from the origin as it had been.

Ignoring everything else, if an inverse square force law is in effect, doubling distance reduces attraction by what factor?
 
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  • #32
jbriggs444 said:
If the test charge is on the surface of this shell
That's where it was in the first place,wasn't it?
 
  • #33
jbriggs444 said:
Somewhere else within this cloud of charge we have a test charge.
We measure the distance from the origin to the test charge.
We call this distance "r".
We draw an imaginary spherical shell that is centered on the origin and has radius r.
gracy said:
That's where it was in the first place,wasn't it?
 
  • #34
jbriggs444 said:
Somewhere else within this cloud of charge we have a test charge.
We measure the distance from the origin to the test charge.
We call this distance "r".
We draw an imaginary spherical shell that is centered on the origin and has radius r.
jbriggs444 said:
If the test charge is on the surface of this shell
gracy said:
That's where it was in the first place,wasn't it?
wasn't it.png
 
  • #35
jbriggs444 said:
t is now twice as far from the origin as it had been.
jbriggs444 said:
if an inverse square force law is in effect, doubling distance reduces attraction by what factor?
4 times.
 
  • #36
gracy said:
4 times.
So if you put that together, moving the test charge to twice its original distance, the charge enclosed by a spherical shell centered on the origin and just touching the test charge has increased by a factor of 8. Due to inverse square, the attraction induced by a given charge has decreased by a factor of 4.

By what factor has the attraction of the test charge to the enclosed charge increased or decreased? Has it increased? Has it decreased?
 
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  • #37
what about my post #34?
 
  • #38
gracy said:
what about my post #34?
What about it?
 
  • #39
correct or not?What's wrong n it?where am I missing?
 
  • #40
gracy said:
correct or not?What's wrong n it?where am I missing?
Your post 34 does not make a statement. How can it be right or wrong?
 
  • #41
gracy said:
where am I missing?
What's wrong in it?Clear my doubt.
 
  • #42
gracy said:
What's wrong in it?Clear my doubt.
Asked and answered. It is neither right nor wrong because it makes no statement.
 
  • #43
jbriggs444 said:
If the test charge is on the surface of this shell, it is now twice as far from the origin as it had been.
How?As per my understanding ,it is at the same distance.r is not doubled.
 
  • #44
We increased the size of the shell and we moved the test charge.

Edit: Hence the words "had been" -- to emphasize that something changed.
 
  • #45
jbriggs444 said:
By what factor has the attraction of the test charge to the enclosed charge increased or decreased?
increased ,2 times..
 
  • #46
gracy said:
increased ,2 times..
Right.

Now, generalize this. Is the attraction of the test charge toward the origin proportional to its distance, r, from the origin?
 
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  • #47
jbriggs444 said:
Now, generalize this. Is the attraction of the test charge toward the origin proportional to its distance, r, from the origin?
yes.
 
  • #48
gracy said:
yes.
Is this the same relationship that holds for simple harmonic motion -- that attraction toward the equilibrium point is proportional to displacement from the equilibrium point?
 
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  • #49
jbriggs444 said:
Is this the same relationship that holds for simple harmonic motion -- that attraction toward the equilibrium point is proportional to displacement from the equilibrium point?
yes.but what happens when it reaches at origin??
 
  • #50
Why should anything happen? There's nothing at the origin but more of the same uniform charge cloud that surrounds the origin.
 
  • #51
I mean will the charge go to the other side of the origin?
 
  • #52
gracy said:
I mean will the charge go to the other side of the origin?
I have been implicitly assuming that the test charge is on an object with some non-zero mass. (A reasonable assumption because all charged objects have non-zero mass).

What is the force on the test charge at the origin? What does Newton's first law have to say?
 
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  • #53
jbriggs444 said:
What is the force on the test charge at the origin? What does Newton's first law have to say?
mass into acceleration
 
  • #54
No. That is a mangling of Newton's second law. Please try again.
 
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  • #55
oh,sorry.First law,ok.It says An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
 
  • #56
And the first part of my question asked about the force on the test charge at the origin. Can you answer that?
 
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  • #57
As origin is equilibrium position total force has to be zero,but that's what I want to ask why this center of charge i..e origin is equilibrium position?
 
  • #58
You are reasoning backwards.

You are apparently not yet convinced that the origin is an equilibrium position. You cannot argue that force is zero there based on something that you do not even believe to be true. Instead, you need to convince yourself that force is zero there.

So... What is the total electrostatic force on the test charge when it is in the center of a uniform spherical cloud of charge?
 
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  • #59
jbriggs444 said:
So... What is the total electrostatic force on the test charge when it is in the center of a uniform spherical cloud of charge?
I now understand force from both side will cancel each other.Resultant force will be zero.
 
  • #60
gracy said:
As origin is equilibrium position total force has to be zero
gracy said:
I mean will the charge go to the other side of the origin?
Is the answer no then?
 

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