This MIT problem is confusing me

[flyingpig]

Homework Statement

http://ocw.mit.edu/courses/physics/8-02-electricity-and-magnetism-spring-2002/assignments/ps2a.pdf

Go to the first problem part a)

Now look at the solutions

http://ocw.mit.edu/courses/physics/8-02-electricity-and-magnetism-spring-2002/assignments/pss2.pdf


It says that the E-field inside the metal is 0. Why? I thought that only applies when it is charged. This metal is uncharged

 

[Andrew Mason]

It says that the E-field inside the metal is 0. Why? I thought that only applies when it is charged. This metal is uncharged

The charges in the conductor are free to move in response to even the slightest electric field. So, if the field inside the metal was not 0, the charges in the metal would keep moving in response to the field until it was reduced to 0. Since the charges cannot go further than the surfaces, that is where they must reside.

Imagine a Gaussian sphere through the middle of the conductor (ie. enclosing the inside surface only). What charge must be on the inner surface of the conductor in order to make the flux through the Gaussian sphere in the middle 0?

AM

 

[SammyS]

...

It says that the E-field inside the metal is 0. Why? I thought that only applies when it is charged. This metal is uncharged

No. The E field in a conductor is 0. Even in the case when the conductor is charged.

How would adding a charge to a conductor in which the E field was non-zero -- perhaps even an itty-bitty charge -- suddenly make the E field become zero?

 

[flyingpig]

Isn't this all under the case of static equilibrium? How do we always know it is under equilibrium?

PF's lag prevented me from responding the last two days...

 

[flyingpig]

No. The E field in a conductor is 0. Even in the case when the conductor is charged.

How would adding a charge to a conductor in which the E field was non-zero -- perhaps even an itty-bitty charge -- suddenly make the E field become zero?

No, not adding a charge. Charging it would create a quick external field and such that the charges then will align themselves to zero the field inside and leeving the excess charges on the surface.

 

[Andrew Mason]

No, not adding a charge. Charging it would create a quick external field and such that the charges then will align themselves to zero the field inside and leaving the excess charges on the surface.

Exactly. A simple application of Gauss' law shows that all the charge must reside on the outer surface of the conducting sphere.

AM

 

[SammyS]

Isn't this all under the case of static equilibrium? How do we always know it is under equilibrium?

PF's lag prevented me from responding the last two days...

You had that problem too? I thought maybe my computer was biting the dust.

No, not adding a charge. Charging it would create a quick external field and such that the charges then will align themselves to zero the field inside and leaving the excess charges on the surface.

It's true that immediately after introducing the charge into the hollow region, there will be a momentary E field in the conducting material. However, free charges (in this case, electrons) move rapidly and equilibrium is reestablished --- among other things, the E field will be zero within the conducting material of the sphere. According to your textbook, it takes about 10^-16 seconds, or less, to reestablish equilibrium after the charge is suddenly introduced.

You can pretty well assume that the problems you are trying to solve at this level all deal with electrostatics.

 

[flyingpig]

No but we are talking about when the charge isn't introduced yet, when it is uncharged

 

[SammyS]

No but we are talking about when the charge isn't introduced yet, when it is uncharged

There is zero net charge everywhere, the conductor being neutral. Why would there be a field within the conductor?

 

[flyingpig]

There is zero net charge everywhere, the conductor being neutral. Why would there be a field within the conductor?

So that electrons can freely roam inside. When you charge it, then all the charge goes out on the surface

 

[SammyS]

If you charge the conductor itself, all the excess charge goes to the outside surface.

 

[flyingpig]

If you charge the conductor itself, all the excess charge goes to the outside surface.

Yes that's what I meant, but that's only if I charge it. If I don't charge it, nothing happens, as in the "excess" charges won't all go out on the surface

 

[SammyS]

If it's neutral, then there is no excess charge.

I'd volunteer what happens when you place a charge inside, but I'll wait for you to ask.

 

[flyingpig]

There could be excess charge, but their net charge is 0 and it would still be neutral

 

[flyingpig]

Am I impossible? Lol

 

[flyingpig]

Sorry to bring this up now

If the conductor was uncharged, the charges are still bound to move, the net charge wouldn't be 0 right? It is only that I charge it that I create an external E-field to make the field inside the conductor 0. When it is uncharged the charges are all still chaotically moving

 

[Andrew Mason]

Sorry to bring this up now

If the conductor was uncharged, the charges are still bound to move, the net charge wouldn't be 0 right?

If the net charge was not 0 then it would not be uncharged. An uncharged conductor means that there is 0 net charge in or on the conductor.

It is only that I charge it that I create an external E-field to make the field inside the conductor 0. When it is uncharged the charges are all still chaotically moving

I don't follow what you are saying there. An uncharged conductor is one that has equal number of + and - charges: net charge = 0. If those charges move around randomly inside the conductor due to thermal motion, that does not change the total charge. An uncharged conductor with no external field has 0 field inside the conductor. There may be microscopic motions of charges due to electric fields create by local anomalies, but macroscopically the field is 0.

AM