Conducting shell conceptual question

[tsuyoihikari]

Homework Statement

A thick-walled, conducting spherical shell has charge q = +10 mC, inner radius R1 = 10cm, and outer radius R2 = 50 cm. A point charge Q = -20 mC is located at the center of the shell.

Describe the the charge distribution in the shell.


2. Given answer

+20 mC on the inner surface; zero charge in the interior of the sphere; -10 mC on the outer surface.

The Attempt at a Solution

I know that there can be no net charge with a gaussian surface drawn inside a conductor, so in order to balance out the point charge, there must be +20 mC of charge on the inner surface, and then there should be a net charge of +10 mC on the whole sphere, so there would be +10 mC on the outer surface. I don't understand why the charge in the interior is zero; shouldn't it be -20 mC because of the point charge?

 

[Delphi51]

I think your argument is correct. The "zero charge in the interior of the sphere" likely means no charge in the metal of the shell, not in the empty space inside the shell.

 

[tsuyoihikari]

But then what would the charge on the outer surface be? Would it be +10 mC or -10 mC?

With my logic, it should be +10 mC, but the answer gives -10 mC.

 

[cupid.callin]

It will be -10 mC.

As the net charge on shell is +10 mC and charge on inside surface is +20mC
so let charge on outside surface is X

therefore, X + 20 = 10

so X = -10mC

 

[tsuyoihikari]

oh okay, so charge on shell doesn't include charge in the very center at all.
Thank you very much Delphi51 and cupid.callin!

 

[cupid.callin]

Ans for your problem of net charge in a conductor, check this: https://www.physicsforums.com/showthread.php?t=118167