Coulomb atraction inside a charged sphere

Question

There is a hollow metallic sphere, positively charged. And inside of it there is a much smaller sphere, negatively charged. The question is: will the walls of the bigger sphere attract the smaller sphere inside?

There are two ways of thinking on this.
The fist one is to consider the bigger sphere without anything inside it. Place an imaginary gaussian surface inside the empty sphere. If the surface doesn't enclose any charge, there are no lines of electric field passing through the surface. Thus, there is no electric field in any point inside the positively charged hollow sphere. Since there is no electric field, if a test charge is put inside, there will be no electric force acting on it.

The second way of thinking is as follows. Consider each point of the positively charged hollow sphere as an individual charge, which attracts the negative charge inside. If the negative charge inside the hollow sphere is off the center, then the sum of the attractive forces due to all the points of the wall won't be balanced . Thus, attraction will occur.

So, which answer is correct, will it attract or not?

Answer 1

You are right that without the negative charge inside, the positive charge on the outer conducting shell will distribute evenly and that there will be no electric field inside the shell.

If we kept that uniform distribution "frozen", then the negative charge could move anywhere inside the shell and not feel any net force.

However, you made the shell a conductor, so the positive charges can move due to the presence of the negative charge on the inside. So yes, if you move he negative charge off center, while it initially has a net force of 0 acting on it, it will also pull the positive charges closer to it, and then soon be attracted to that imbalanced positive charge.