Electric field inside hollow conductor with a charge

[Tiago3434]

Ok, this might be a really dumb question, but I still am asking it: I was reading about gauss' Law when it comes to a hollow conductor with a (say) point charge inside it, and it seems intuitive to me that, in electrostatic equilibrium, the charges rearrange themselves to cancel the electric field inside it, after all, if there were a nonzero electric field, there would be acceleration, which violates the idea that the system is in electrostatic equilibrium. Here is the q: is there a reason (or intuition, perhaps) as to why the charges don't rearrange themselves to cancel all electric field inside it, including inside the cavity, where the point charge lies?

 

[NFuller]

For this to happen, you would need a charge density in the shell which produces an electric field inside the shell with the form $-kq/r^{2}\;\hat{r}$ to cancel out the electric field from the point charge. However, there is no arrangement of charge density in a spherical shell which can produce such an electric field inside the shell.

 

[pixel]

...after all, if there were a nonzero electric field, there would be acceleration, which violates the idea that the system is in electrostatic equilibrium.

A charge is not affected by the electric field that it produces, so no acceleration.

 

[x_engineer]

The charges can't go just anywhere. By definition of a "hollow" conductor, they are constrained to move only inside the conductor. If not, they would move to the place where you placed your internal charge and cancel it out.