The discussion revolves around the motion of a charge -Q in relation to its distance from the center of a uniformly charged sphere. Participants explore the differences between oscillatory motion and simple harmonic motion (SHM), particularly how the distance from the center influences the type of motion exhibited by the charge. The conversation includes theoretical considerations and interpretations of force laws.
Participants generally agree on the application of the spherical shell theorem and its implications for the net electrical field. However, there remains some confusion and lack of consensus regarding the definitions and implications of oscillatory motion versus SHM, as well as the specific relationships between the distances and charges discussed.
Some participants express uncertainty about the definitions of variables and the implications of the spherical shell theorem in this context. The discussion includes unresolved mathematical relationships and assumptions regarding the charge distribution and its effects on motion.
What is at the origin to cause this? What, in your opinion distinguishes "oscillatory and periodic" motion from simple harmonic motion?gracy said: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?
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.jbriggs444 said:oscillatory and periodic" motion from simple harmonic motion?
This is coulomb's force,I know.jbriggs444 said:A charge far away sees an inverse square force law (-1/r^2)
But I don't know which force are you talking about here?jbriggs444 said:and a charge located within the cloud sees a force law that is directly proportional to distance (-r)
The Coulomb force.gracy said:This is coulomb's force,I know.
But I don't know which force are you talking about here?
but it is for gravitation.jbriggs444 said:spherical shell theorem
That is for any force that follows an inverse square law.gracy said:but it is for gravitation.
could you please elaborate this part?jbriggs444 said: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.
That means overall(total) charge can be treated as/assumed to be concentrated at a point at its centre.jbriggs444 said:spherical shell theorem
You meant centre of the sphere.jbriggs444 said:on the origin
Right.gracy said:That means overall(total) charge can be treated as/assumed to be concentrated at a point at its centre.
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).gracy said:You meant centre of the sphere.
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 rjbriggs444 said:the portion of the charge cloud farther from the origin than the -Q test charge
That is nonsense. You stated that -Q is a quantity of charge. It cannot also be a distance.gracy said: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?
Where i said -Q is distance?jbriggs444 said:It cannot also be a distance.
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.jbriggs444 said:That is nonsense. You stated that -Q is a quantity of charge. It cannot also be a distance.
yesjbriggs444 said:You mean the distance from the origin to the charge whose value is -Q. And you want to denote that as a.
jbriggs444 said: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.
What is it that you would like clarified?gracy said:please make it more clear.It's my humble request
yes.jbriggs444 said:Do you agree that if this cloud of charge is spherical then the portion which is farther than r from the origin produces no net electrical field on the test charge? The spherical shell theorem should tell you this?
yesjbriggs444 said:Do you agree that the field from the portion of the could which is nearer than r from the origin produces an electrical field on the test charge identical to that which would be produced if its entire charge were concentrated at the origin? The spherical shell theorem should also tell you this.
I am so sorry ;did not get you.jbriggs444 said:So you agree that if we have a uniform cloud of charge centered on the origin and a test charge at distance r from the origin that the total charge closer to the origin than the test charge is proportional to r3
Should I think of coordinate system.jbriggs444 said:So you agree that if we have a uniform cloud of charge centered on the origin and a test charge at distance r from the origin that the total charge closer to the origin than the test charge is proportional to r3
Yes.I understand it now .jbriggs444 said:So you agree that if we have a uniform cloud of charge centered on the origin and a test charge at distance r from the origin that the total charge closer to the origin than the test charge is proportional to r3
How does it answer my OP?jbriggs444 said:So you agree that if we have a uniform cloud of charge centered on the origin and a test charge at distance r from the origin that the total charge closer to the origin than the test charge is proportional to r3
Do you agree that if this cloud of charge is spherical then the portion which is farther than r from the origin produces no net electrical field on the test charge? The spherical shell theorem should tell you this.
Do you agree that the field from the portion of the could which is nearer than r from the origin produces an electrical field on the test charge identical to that which would be produced if its entire charge were concentrated at the origin? The spherical shell theorem should also tell you this.
No. The coordinate system is irrelevant.gracy said:Should I think of coordinate system.
Your OP was unclear. I had to guess what you were talking about. 27 posts later and you still have not clarified it.gracy said:How does it answer my OP?
8 times?jbriggs444 said:If you keep everything else constant and double r, by what factor will the amount of enclosed charge have increased?