# How the distance from centre decides type of charge motion?

1. Sep 24, 2015

### gracy

If charge -Q of mass m is kept on y axis at large distance from the center,then it will execute oscillatory and periodic motion but if it is released very close to the origin then it will execute SHM .I want to know why?I mean how the distance from centre decides type of motion oscillatory or SHM?

2. Sep 24, 2015

### jbriggs444

What is at the origin to cause this? What, in your opinion distinguishes "oscillatory and periodic" motion from simple harmonic motion?

Edit: at a guess, we have a diffuse, spherically symmetric cloud with a uniform positive charge density centered on the origin. A charge far away sees an inverse square force law (-1/r^2) and a charge located within the cloud sees a force law that is directly proportional to distance (-r).

3. Sep 24, 2015

### gracy

Both are periodic. The basic difference between the two is that in shm acceleration is directly proportional to displacement which is not there in case of oscillation.

4. Sep 24, 2015

### gracy

This is coulomb's force,I know.
But I don't know which force are you talking about here?

5. Sep 25, 2015

### jbriggs444

The Coulomb force.

According to the spherical shell theorem, the portion of the charge cloud farther from the origin than the -Q test charge cancels out to a net of zero. So only the portion of the cloud nearer the origin than the test charge matters. That portion of the cloud has volume proportional to r3 and inverse square attraction proportional to 1/r2. That means that the net attraction is proportional to r.

6. Sep 25, 2015

### gracy

but it is for gravitation.

7. Sep 25, 2015

### jbriggs444

That is for any force that follows an inverse square law.

8. Sep 25, 2015

### gracy

Ok.Please don't go anywhere.I have to some queries.

9. Sep 25, 2015

### gracy

could you please elaborate this part?

10. Sep 25, 2015

### gracy

That means overall(total) charge can be treated as/assumed to be concentrated at a point at its centre.

11. Sep 25, 2015

### gracy

You meant centre of the sphere.

12. Sep 25, 2015

### jbriggs444

Right.

Uniform charge density. Sphere with volume that goes as r3. So total enclosed charge proportional to r3. Field equivalent to that charge at origin. Inverse square force law. So net field strength at radius r scales as r3/r2.

13. Sep 25, 2015

### jbriggs444

Yes, as in post #2, I am guessing that you are discussing a situation with a cloud of charge of uniform density centered at the origin. The center of a sphere of radius r centered at the origin is at the origin (by definition).

14. Sep 25, 2015

### gracy

If we take distance of -Q from centre of sphere i.e origin as "a" & the portion of the charge cloud to be q and radius of sphere to be r
let b be any value less than r .If r>b or r>a
that's what it means?

15. Sep 25, 2015

### jbriggs444

That is nonsense. You stated that -Q is a quantity of charge. It cannot also be a distance.

16. Sep 25, 2015

### gracy

Where i said -Q is distance?

17. Sep 25, 2015

### jbriggs444

Edit: I apologize. You mean the distance from the origin to the charge whose value is -Q. And you want to denote that as a. I am not sure what you want q and r and b to denote.

18. Sep 25, 2015

### gracy

yes

19. Sep 25, 2015

### gracy

please make it more clear.It's my humble request

20. Sep 25, 2015

### jbriggs444

What is it that you would like clarified?