Conducting spheres Gauss's law

[bmxicle]

Homework Statement

There are two conducting spheres, one hollow outer sphere which originally had +60nC of charge on it, and a smaller inner sphere enclosed by the hollow outer sphere which contains +20nC of charge.

Homework Equations

INT(E.DA) = Q_enclosed/epsilon₀

The Attempt at a Solution

Well first off obviously the inner sphere has +20nC of charge on it and that can't change. For the outer sphere, if you place a spherical gaussian surface that runs through the middle of the outer sphere the net Q_enclosed must be zero as the Electric field is zero everywhere inside a conductor. So by this there must be -20nC on the inside of the shell and 80nC on the outside of the shell.

Now here comes the part I'm confused by. Isn't there still only +60nC of net charge on the outer sphere? The answer I was given says there is +80nC charge on the outer sphere, but i don't understand how that can be the net charge on the outer sphere.

 

[Doc Al]

Now here comes the part I'm confused by. Isn't there still only +60nC of net charge on the outer sphere? The answer I was given says there is +80nC charge on the outer sphere, but i don't understand how that can be the net charge on the outer sphere.

Are you sure they said that the net charge on the outer sphere was +80nc? In any case, you are correct. But I suspect that the answer key meant that the outer surface had a charge of +80nC.

 

[bmxicle]

That must be what they meant, though the question seems to be somewhat ambiguous. I just wanted to make sure I wasn't making a conceptual error though so it doesn't really matter all that much.

Thanks.

 

[jhae2.718]

I would think this too. The outer surface would have a +80 nC charge as stated, and the net charge would be 60 nC.

Indeed, conservation of charge would require the outer shell to have a net charge of 60 nC.

 

[Doc Al]

That must be what they meant, though the question seems to be somewhat ambiguous.

Just for fun, can you post the question exactly as given?

 

[bmxicle]

"Two pairs of charged, hollow, spherical, conducting shells are connected with wires and switches. The system AB is very far from CD. The radius of each large shell is four times that of the small shell. Before the switches are closed, the small shells have charges of +20nC and the large shells have +60nC. After the switches are closed, rank the net charge on each shell. "

There is also a diagram Where shells A and B with r_a>r_b are connected by a wire, and C encloses shell d. I only wasn't sure about the part I asked about but that was the entire question.

 

[Doc Al]

"Two pairs of charged, hollow, spherical, conducting shells are connected with wires and switches. The system AB is very far from CD. The radius of each large shell is four times that of the small shell. Before the switches are closed, the small shells have charges of +20nC and the large shells have +60nC. After the switches are closed, rank the net charge on each shell. "

The connecting wire makes a difference! (You left that out in your description.) Can I assume that the shells you were talking about were not connected by a wire? (One pair of shells had a wire, the other didn't?)

In any case, you are right. They do seem to ask for the net charge.

 

[bmxicle]

Well in the question i asked, yes they were not connected by a wire, but now that you mention that, that's not what the actual question asked :p and i can now see a very faint partial wire on the diagram.

If they're connected the charge will all go to the outside because it should essentially act as one large conductor with the wire attached so 80nC makes sense.

 

[Doc Al]

If they're connected the charge will all go to the outside because it should essentially act as one large conductor with the wire attached so 80nC makes sense.

Yep, there you go.