Distribution of Charge on a Conducting shell

[fornax]

Homework Statement

A +30mC point charge sits at the center of a spherical thick metal shell, of 4.0cm inner radius, and 2.0cm thickness. The net charge on the shell is -50mC.

Homework Equations

The Attempt at a Solution

I came up with several conclusions and I'm not really sure which one is right. I'm just looking for a confirmation of how this charge would distribute itself. I learned that in such a case as this, an equal and opposite amount of charge would distribute itself across the inner surface of the shell, so -30mC. Since the net charge is then -50mC, that means that -20mC must be on the outer surface. That didn't really make much sense to though me since there is no where for a positive charge on the shell. So does that mean there's a charge of -80mC on the inner surface of the shell, and +30mC on the outside? or is it just one big negatively charged conductor?

 

[ehild]

The shell is negatively charged and the point charge at the centre attracts equal amount of negative charge onto the inner surface of the shell. The remaining negative charge distributes on the outer surface.

ehild

 

[fornax]

Thank you so much, I've been stuck on the rest of the problem. Thank you for clarifying that for me.