How Does a Hollow Conducting Sphere Affect Internal and External Charges?

[IWantToLearn]

A hollow, conducting sphere is initially uncharged. A positive charge, +q₁, is placed inside the sphere (at the center). Then, a second positive charge, +q₂, is placed near the sphere but outside it.

Which of the following statements describes the net electric force on each charge?
1-There is a net electric force on +q₂ but not on +q₁.
2-There is a net electric force on +q₁ but not on +q₂.
3-Both charges are acted on by a net electric force with the same magnitude and in the same direction.
4-Both charges are acted on by a net electric force with the same magnitude but in opposite directions.
5-There is no net electric force on either charge.


Attempt at a solution
I know that for a charged hollow spherical conductor, the charge is distributed on both the inner and outer surface of the conductor, and the net electric field in the material of the conductor is zero, also the net electric field inside the cavity is zero, and the net eelectric field in a point close to the outer surface is δ/ε₀

but in this case there is a point charge at the center of the cavity, and the net electric field inside the cavity must has a nonzero value (due to the point charge).

i thought that both of the charges may cause the spherical conductor to be charged through induction, so the electric field due its charge inside the cavity is zero, and hence choice (1) will be relevant, but i am not sure.

i thought also that if the spherical conductor will remain uncharged, so there will not be a charge distribution in its surface, and the only remaining thing is the coulomb force between the two charges acting on each other, so choice (4) will be relevant.


please help

 

[Liquidxlax]

The charge at the center of the sphere will induce an equal and opposite charge on the inside of the conducting sphere and a equal and same charge on the outside of the sphere.

So what does that tell you?

 

[IWantToLearn]

The charge at the center of the sphere will induce an equal and opposite charge on the inside of the conducting sphere and a equal and same charge on the outside of the sphere.

So what does that tell you?

if so, then the charge at the center will not be affected by the electric field of the induced charge distribution on the inner surface, cause the field inside the cavity is zero,
and the charge outside will be affected by the electric field of the induced charge distribution on the outer surface, if this is the case then choice (1) is the answer

But wait a minute, why not the charge outside the sphere induce a charge distribution on the the sphere similar way to the charge distribution induced by the inner charge
if this is true, then we will have a complex charge distribution, and i can't tell exactly about the force

 

[Liquidxlax]

the charge on the inside the sphere is positive so its field lines will be emitted radially outwards to the negatively charged sphere. There is a field inside the sphere from the positively charged particle

there will be zero force on the particle inside the sphere

Since a positive charge is induced on the outside of the sphere the charge outside the sphere will experience a force

 

[IWantToLearn]

the charge on the inside the sphere is positive so its field lines will be emitted radially outwards to the negatively charged sphere. There is a field inside the sphere from the positively charged particle

there will be zero force on the particle inside the sphere

Since a positive charge is induced on the outside of the sphere the charge outside the sphere will experience a force

again why not the charge outside the sphere causes an induced electric charge distribution on the outer surface, so we have two overlapped charge distributions on the hollow sphere, one due to the inner charge and one due to the outer charge.

by the way the electric field at the center must be zero, and hence the force, so there is no force affecting the charge in the center.