A hollow conductor carries a net charge of ++3QQ. A small charge of −−2QQ is placed inside the cavity in such a way that it is isolated from the conductor. How much charge is on the outer surface of the conductor?

According to the principle of electrostatic shielding, a hollow conductor will shield its interior from any external electric fields. When a charge is placed inside a hollow conductor, the conductor will rearrange its own charges in such a way as to cancel out any electric fields within the cavity created by this internal charge.

As a result, the charge within the cavity induces an equal and opposite charge on its inner surface. Since we have a small charge of −2Q placed inside the cavity, it will induce a charge of +2Q on the inner surface of the conductor. This is to maintain the electrostatic equilibrium inside the conductor.

Now, the net charge on the conductor is +3Q as given. This net charge includes both the charge on the outer surface and the induced charge on the inner surface. The charge on the outer surface is the total charge on the conductor minus the induced charge on the inner surface.

Charge on the outer surface of the conductor = Total charge of the conductor – Induced charge on the inner surface = +3Q – (+2Q) = +3Q – 2Q = +Q

So, the charge on the outer surface of the conductor is +Q.