What are they doing? Charges and Conductors

[flyingpig]

Homework Statement

[PLAIN]http://img823.imageshack.us/img823/236/40553004.png


[PLAIN]http://img717.imageshack.us/img717/1561/15355872.png

The Attempt at a Solution

I am a bit confused isn't the 6.00nC sending its own E-field?

For part b) Why do they say Qinside is 0? They said the placed a 6.00nC charge there?

 

[cupid.callin]

(a) you are right. the 6nC charge creates field inside the conductor (use gauss law)

(b) ...

Who's solution have you given? Isn't it yours?

 

[flyingpig]

(a) you are right. the 6nC charge creates field inside the conductor (use gauss law)

(b) ...

Who's solution have you given? Isn't it yours?

No this isn't mine and I don't understand it. Why is E-field 0 inside when 6nC creates a E-field inside?

 

[cupid.callin]

you are right, there will be field inside conductor (in empty space) but not in the material of conductor !

 

[flyingpig]

you are right, there will be field inside conductor (in empty space) but not in the material of conductor !

But it's hollow?

 

[cupid.callin]

so? does it matter

 

[flyingpig]

so? does it matter

What material? I thought it was hollow?

 

[cupid.callin]

its hollow inside but in the first pic ... where there is dotted line ... tht is the material. there E = 0

 

[SammyS]

Homework Statement

The Attempt at a Solution

I am a bit confused isn't the 6.00nC sending its own E-field?

For part b) Why do they say Qinside is 0? They said the placed a 6.00nC charge there?

flyingpig, I made another attempt to explain why the electric field within conducting material is zero. Find it in your previous https://www.physicsforums.com/showthread.php?p=3119555#post3119555" It's also true that any excess charge on a conductor will only reside on a surface of the conductor. Otherwise, according to Gauss's Law, an excess charge within a conductor would produce a non-zero field in the conductor.

As for the question: "For part b) Why do they say Qinside is 0? They said the placed a 6.00nC charge there?"

If you accept that E = zero in the conducting material, then, E = 0 everywhere on the surface of the sphere with a radius of 1.50 m. Gauss's Law says that the net charge (or excess charge or the sum of the charges) interior to this sphere is zero. In you second image, q_in refers to the net charge inside this sphere.

So, if an isolated charge is placed in the hollow of a conductor, an equal but opposite amount of charge will be distributed along the inner surface of the hollow.
​

 

[flyingpig]

But inside there clearly is a charge 6nC, which is almost like an insulating sphere with a charge of 6nC

The net charge on the conductor (why do they say net charge and not just charge?) is -4nC

I still don't understand

 

[flyingpig]

Sammy, there is one thing I don't understand very well.

When they say "Q^en", where is it enclosed? My book deducts that the E = 0 inside the conductor and hence the Guassian Surface has enclosed a charge of 0? How do they deduct the fact there is a -6nC and a +6nC?

 

[JaWiB]

When they say "Qen", where is it enclosed?

Enclosed by any (imaginary) Gaussian surface you choose to draw. In this case, they drew a Gaussian sphere between the inner and outer surfaces of the conductor.

My book deducts that the E = 0 inside the conductor and hence the Guassian Surface has enclosed a charge of 0? How do they deduct the fact there is a -6nC and a +6nC?

Since E=0, you know that the charge enclosed by the Gaussian sphere must be zero, by Gauss's law. But you also know that there is a +6nC charge at the center (in the vacuum), so logically there must be a -6nC charge somewhere else inside your Gaussian sphere, and that must be at the inner surface since (1) it can't be in the vacuum (there are no other charges there!) and (2) you can draw your Guassian sphere arbitrarily close to the inner surface and still have a zero electric field.

 

[SammyS]

But inside there clearly is a charge 6nC, which is almost like an insulating sphere with a charge of 6nC

The net charge on the conductor (why do they say net charge and not just charge?) is -4nC

I still don't understand

They say net charge because each atom of the conductor has a positively charged nucleus surrounded by a cloud of negatively charged electrons. There are lots and lots of atoms making up the conductors, so the total amount of positive charge is huge. So is the total amount of negative charge. For the most part these charges cancel.

The author uses the term net charge to emphasize this point.

Sammy, there is one thing I don't understand very well.

When they say "Q_in", where is it enclosed? My book [STRIKE]deducts[/STRIKE] deduces that the E = 0 inside the conductor and hence the Gaussian Surface has enclosed a charge of 0? How do they deduct the fact there is a -6nC and a +6nC?

Yes, Serway makes a rather convincing argument that the electric field within a conducting material is zero (E = 0) under static conditions. Also, he concludes that any excess (net) charge must reside on the surface of a conductor.

Once the fact that E=0 in the conducting material, your author (Serway) uses that fact ( E = 0) for a Gaussian surface which is completely embedded in the conductor to know that the flux through that surface is zero. Therefore, according to Gauss's Law, the net charge, Q_in enclosed by this surface is zero.

(The reason he says net charge: There likely are billions of billions of coulombs of positive charge (and a similar amount of negative) enclosed within this surface.)​

Since there is an isolated sphere with a net charge of 6 nC at the center of the shell, there must be a charge of ‒6 nC on the inner surface of the spherical shell. There's no other place it can be & it's the only way to get Q_in = 0 .

Is this beginning to make sense? It's important to understand the order in which elements of this argument build on each other.

 

[flyingpig]

Since E=0, you know that the charge enclosed by the Gaussian sphere must be zero, by Gauss's law.

I thought that only meant that part of the surface has charges of 0, but everywhere.

 

[SammyS]

Q_in is everything enclosed by the Gaussian surface.

 

[flyingpig]

Q_in is everything enclosed by the Gaussian surface.

but that is deduced from just the surface of the Gaussian surface - inside the conductor.

 

[SammyS]

but that is deduced from just the surface of the Gaussian surface - inside the conductor.

Electric flux is through the surface. The charge is enclosed INSIDE the surface.

Electric flux and electric charge are two very different things. Gauss's Law simply relates the two.

 

[JaWiB]

Yup, it's like if I had a chicken coop and I wanted to know how many chickens were in the coop without looking inside. I could look at all the entrances and exits and see how many eggs were coming out of the coop ("egg flux"), and figure out how many chickens were inside; if no eggs came out, then there must not be any chickens inside.

(Get it? The chicken is a source of eggs just like a point charge is a source of electric field...)

 

[flyingpig]

Does that mean if this Gaussian Surface is real and if I were to go outside the surface of the surface, then the E field is still 0?

 

[SammyS]

Does that mean if this Gaussian Surface is real and if I were to go outside the surface of the surface, then the E field is still 0?

What do you mean by real ?

If there is zero net charge within the surface, that does not mean that E = 0 everywhere on the surface, it merely means that the net flux through the surface is zero - as much goes in as comes out.

 

[flyingpig]

I have another problem

A spherical conductor of charge 30uC and radius 15cm. Find the E-field and Electric Potential at radius a) r = 10cm b) 20cm

For a) Do we assume the conductor is in electrostatic equilibrium and therefore must be 0? If I were to follow a textbook approach, I will say it is immediately 0. When they mean the charge is 30uC, does that mean it is the net charge? I guess what I am trying to say is, IS IT EVEN 0?

 

[JaWiB]

Keep in mind 20cm puts you outside the conductor. Also, convention is that the potential is set to zero infinitely far from a localized charge distribution, so even if you find the electric field is zero you don't know the potential.

I would also assume the 30uC means net charge

 

[flyingpig]

Personally I think it does matter with "net charge" as opposed to "charge", is it just that I am picky or does the answer really change?

 

[flyingpig]

Wait, just going back, the E-field that is 0 inside meant the net E-field right?

 

[JaWiB]

Personally I think it does matter with "net charge" as opposed to "charge", is it just that I am picky or does the answer really change?

Well, to be specific you should say net charge. Any object really has a huge amount of protons (positive charges) and electrons (negative charges), so if I said my desk has 30nC of charge I could just be referring to some of the protons in my desk. But no one would say it with that meaning, so it's kind of a moot point.

Wait, just going back, the E-field that is 0 inside meant the net E-field right?

Yes. All the charges in the object create their own electric fields, but they rearrange themselves so that all those fields add up to zero. (And if there's an external field, they rearrange themselves so that field gets canceled out as well)

 

[SammyS]

Yes. All the charges in the object create their own electric fields, but they rearrange themselves so that all those fields add up to zero. (And if there's an external field, they rearrange themselves so that field gets canceled out as well)

Yes, These charges are exceedingly smart. They must pass several high level physics courses before they're ever allowed to be inserted into a conductor.