How the distance from centre decides type of charge motion?

[gracy]

Sir,please say "yes" to my post #69.

 

[jbriggs444]

I think the answer to my question in previous post is no.Because if spherical shell theorem were to be applicable in both cases then for bigger /larger r also the motion will be simple harmonic motion which is not the fact as depicted in my OP.Right?

The spherical shell theorem is a theorem. It always applies as long as its premises hold. They do hold in the case of large r.

In particular:

1. The net force from the portion of the charged cloud outside the shell of radius r is zero.
2. The net force from the portion of the charged cloud inside the shell of radius r is equivalent to the force that would exist if the charge were concentrated at the origin.

 

[gracy]

Then why not in this case?

 

[gracy]

Oh! I thought I understood the whole thing.

 

[jbriggs444]

Then why not in this case?

Re-read post #60 and, in particular, the edit there.

Edit: 70, darnit.

 

[gracy]

post 60?it's mine.

 

[jbriggs444]

post 60?it's mine.

Yeah, yeah, I corrected myself but you were just too quick.

 

[gracy]

Oh! I thought I understood the whole thing.

I was correct in thinking so!

 

[gracy]

Ok.With all credits to you I now understand why in case of big r it will not be simple hatmonic motion but why it would be periodic anyway?

 

[jbriggs444]

Ok.With all credits to you I now understand why in case of big r it will not be simple hatmonic motion but why it would be periodic anyway?

It seems intuitively obvious. But let me see if I can come up with a solid and understandable argument...

We are working in one dimension. The only forces present are along the x axis. So there are no side to side complications to worry about.

We are dealing with a central force that depends only on distance from the origin. That means that we are working in a conservative field. However, let's try a more elementary argument than that. How about time reversal symmetry...

We know we have an attractive force. If the test charge is ever motionless or if it is ever moving toward the origin, it will pass through the origin. Let us hand-wave away the case where the test charge is moving at a speed greater than or equal to escape velocity and never hits the origin.

When the test mass passes through the origin, it will go outward for some distance, turn around and fall back. [Remember that we hand-waved away the possibility of escape]

On its path back to the origin, its acceleration at each r value on the way in will be equal to its acceleration at that r value on the way out. It will have the same inward velocity at each r value on the way in as it had on its way out. It will return to the origin at the same speed it left. The time taken for that trip is purely a function of its speed at the origin. And its speed each time it passes through the origin is identical.

It follows that its trajectory is periodic.

 

[gracy]

I understood it.Thanks Thanks Thanks.You just made my day I was worried throughout the day for this problem.Now I can be relax.Just because of you.You were so patient throughout this thread coping with my silly questions.Thanks again.All the helpers here on physics forum are doing selfless help which is remarkable.Love physics forum!

 

[jbriggs444]

The thank you's make it all worth while.

 

[gracy]

Your avatar/profile pic suggests it's your pleasure

 

[jbriggs444]

Who, me? I know nothing. Nothing. The commandant says that there is to be no fraternizing with the prisoners.

 

[gracy]

Who, me? I know nothing. Nothing. The commandant says that there is to be no fraternizing with the prisoners.

Oooooooooooooo!THAT'S WHAT YOU KEEP SAYING!