(a) A point charge q is inside a cavity in an uncharged conductor (Fig. 2.45). Is the force on q necessarily zero?11
(b) Is the force between a point charge and a nearby uncharged conductor always attractive?12
Reference figure 2.45
Step 1 of 2:
Consider an uncharged conductor having a cavity and a point charge is placed inside it. We are going to find the force acting on the charge. The force on the point charge is not zero. Because the point charge induces the opposite charge on the wall and it will experience an attractive force.
The answer is No.