Charge on spherical conducting shells

[toothpaste666]

Homework Statement

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There are two spherical conducting shells one inside the other. If the total charge on the inside shell is -3q and the total charge on the outside shell is +5q what's is the charge on the inner and outer surface of each shell?

Attempt at solution

My teacher said i can assume there is no charge in the center so i think the inner surface of the small shell has a charge of -6q and the outer surface +3q and the larger shell has inner surface charge of -3q and outer surface charge of +8q

 

[BvU]

Hello TP,

I grant you that this isn't about relevant equations. So the 2 from the template can be left out. But thinking up a solution isn't physics. What are your considerations to come to e.g. this -6 q ?

 

[toothpaste666]

Since there is no charge in the center i wanted to use the smallest numbers that could make the net charge cancel to negative three. I know inside the conductor must be 0 so the charge is on the surfaces so i picked -6 for the inside surface and positive 3 for the outside

 

[BvU]

Wouldn't the -6 q race to the outer surface in a flash ? All the little charge carriers repel each other like crazy and they want to sit as far away from each other as possible !

Remember that inside a conductor there is no electric field: if there were, the charge carriers would simply move with the field until either the field is zero or they can't go any further !

Do you know about Gauss's law ?

 

[toothpaste666]

the internmost charge is the same as the one on the outer surface?

 

[BvU]

Still don't know if you know about Gauss's law. Let's assume you do. Else look it up, e.g. on hyperphysics.

Imagine a gauss sphere halfway inner and outer surfaces of the inner shell. No field (it's a conductor) hence no (net) charge within. No charge inside the inner surface, so no charge on the inner surface either. Conclusion: on the outer surface of the inner shell there is sitting -3q .

Now it's your turn to find out how much charge is sitting on the inner surface of the outer shell ...

 

[toothpaste666]

Oops sorry I do know gausses law and I know the electric field would be E = Qencl/ε4πr^2 it is the Qencl I am having trouble with.
I was confused because I though that if there was charge on one surface then there must be charge on the other one. If the only charge on the inner sphere is -3q on the outer surface then the inner surface of the outer sphere would have a +3q charge and the outer surface of the outer sphere would have a + 2q charge. this also confused me when i was trying the problem on my own because I thought the same polarity of charge could not be on both surfaces of the conductor

 

[BvU]

The shells are prepared by charging (they are not neutral and not connected to ground). The distribution is as you now describe: the +3 is pulled inwards. That way a Gauss suface halfway inner and outer surfaces of the outer shell encloses zero Coulomb: no flux, no E field inside that conductor. The remaining +2 is distributed evenly over the outer surface of the outer shell (*). The outside world observes +2, e.g. using Gauss. (and has no way of telling what's inside !).(*) even if the inner shell isn't centered wrt the outer. Clear from Gauss's law and the outer shell being a conductor !

 

[toothpaste666]

thank you!